a) Mitch has approximately 50 seconds to figure out how to survive before the rocket reaches him, calculated by dividing the distance of 1000 meters by the rocket's velocity of 20 m/s.
b) The rocket will intersect with Mitch at a height of approximately 1050 meters above the ground, calculated by adding the rocket's vertical distance traveled to Mitch's initial height of 1000 meters.
a) To calculate the time Mitch has, we can use the equation of motion for vertical displacement: Δy = v_iy * t + (1/2) * a * t², where Δy is the vertical displacement, v_iy is the initial vertical velocity, t is the time, and a is the acceleration. Since Mitch is at terminal velocity, his vertical velocity is zero (v_iy = 0), and the only force acting on him is gravity (a = -9.8 m/s²). Plugging in the values, we have:
1000 m = 0 * t + (1/2) * (-9.8 m/s²) * t²
Solving this quadratic equation, we find t ≈ 14.3 seconds.
b) To find the location where the rocket intersects with Mitch, we can use the equation of motion for vertical displacement again. Since the initial vertical velocity of the rocket is 125 m/s and the acceleration is -9.8 m/s², and we want to find the displacement when the time is 14.3 seconds, we have:
Δy = v_iy * t + (1/2) * a * t²
Δy = 125 m/s * 14.3 s + (1/2) * (-9.8 m/s²) * (14.3 s)²
Simplifying this expression gives Δy ≈ 895 m.
Therefore, the rocket will intersect with Mitch when he is approximately 895 meters above the ground.
Learn more about rocket's velocity here
https://brainly.com/question/27797265
#SPJ11
Maryum is at a safari park in Tanzania when she sees a herd of running wildebeest about 350 m away from her. Like any curious scientist, Maryum has measured the average sound level produced by various packs and single animals at the park. She wants to figure out how many wildebeest are in this herd so she checks her notes and finds that one running wildebeest at this distance would produce a sound level of 12 dB. She measures the sound level this herd makes to be roughly 24 dB. How many wildebeest are in this herd? (Round your answer to the nearest integer.)
Maryum is at a safari park in Tanzania when she sees a herd of running wildebeest about 350 m away from her.
She measures the sound level this herd makes to be roughly 24 db.
If one running wildebeest at this distance would produce a sound level of 12 dB,
she can find out how many wildebeests are there in the herd.
Suppose there are 'n' wildebeests in the herd.
So,
the sound intensity produced by n wildebeests will be:
Sound intensity
[tex](I) = K / d²[/tex]
where
[tex]I = 10^(-12) W/m² (threshold of hearing), K = 10^(-12) W/m² and d = 350 m[/tex]
For one wildebeest, the sound intensity is given by:
[tex]I1 = K / d1²[/tex]
where [tex]d1 = distance from one wildebeest = 350 m/ nI1 = K / (350/n)²... (1)[/tex]
Let the total sound intensity produced by n wildebeests be I2, then,
[tex]I2 = nI1I2 = nK / (350/n)²... (2)[/tex]
Now, the intensity of sound is proportional to the square of the sound level.
To know more about Tanzania visit:
https://brainly.com/question/33278083
#SPJ11
A 15Ω resistor is connected in series to a 120V generator and two 10Ω resistors connected in parallel to each other. a. What is the total resistance? _____ b. What is the circuit’s current? _____ c. What is the current in one of the _____ 10Ω resistors? d. What is the potential difference across the 15Ω resistor?
a. To find the total resistance, we need to consider the resistors connected in series and in parallel. The 15Ω resistor is connected in series, so we simply add its resistance to the total. The two 10Ω resistors are connected in parallel, so we need to calculate the equivalent resistance of the parallel combination.
To find the equivalent resistance of two resistors in parallel, we use the formula:
1/Req = 1/R1 + 1/R2
Substituting the values, we have:
1/Req = 1/10 + 1/10
Simplifying, we get:
1/Req = 2/10
1/Req = 1/5
So, Req = 5Ω
Now, we can calculate the total resistance by adding the resistance of the 15Ω resistor and the equivalent resistance of the parallel combination:
Total resistance
= 15Ω + 5Ω = 20Ω
b. To find the circuit's current, we can use Ohm's Law, which states that current (I) is equal to voltage (V) divided by resistance (R). The voltage in the circuit is given as 120V, and the total resistance is 20Ω. So, we have:
I = V/R = 120V/20Ω = 6A
Therefore, the circuit's current is 6A.
c. Since the two 10Ω resistors are connected in parallel, they have the same potential difference across them. Therefore, the current in each of the 10Ω resistors is the same as the circuit's current, which is 6A.
d. To find the potential difference across the 15Ω resistor, we can again use Ohm's Law. The current flowing through the circuit is 6A, and the resistance of the 15Ω resistor is given as 15Ω. So, we have:
V = I * R = 6A * 15Ω = 90V
Therefore, the potential difference across the 15Ω resistor is 90V.
In summary:
a. The total resistance is 20Ω.
b. The circuit's current is 6A.
c. The current in each of the 10Ω resistors is 6A.
d. The potential difference across the 15Ω resistor is 90V.
To know more about resistance visit:
https://brainly.com/question/33728800
#SPJ11
A car of mass m moving at a speed vi collides and couples with the back of a truck of mass 2 m moving initially in the same direction as the car at a lower speed v_2. (a) What is the speed v_f of the two vehicles immediately after the collision? (b) What is the change in kinetic energy of the cartruck system in the collision?
The speed of the two vehicles immediately after the collision is (2/3) vi, and the change in kinetic energy of the car-truck system in the collision is -2/3 (mvᵢ²).
A car of mass m is moving at a speed vᵢ, and it collides and couples with the back of a truck of mass 2m that is moving initially in the same direction as the car at a lower speed v₂. The velocity of the center of mass is conserved before and after the collision. This suggests that the sum of the momenta is conserved.
Since the car and the truck move as a single unit after the collision, the velocity of the car-truck combination is V. We can say that:
mvᵢ + 2mv₂ = (m + 2m)V
V = (mvᵢ + 2mv₂)/3m
The kinetic energy of the car before the collision is 1/2 mvᵢ², and the kinetic energy of the truck is 1/2 (2m) v₂² = m v₂². Since the two objects combine into a single unit after the collision, the total kinetic energy after the collision is:
(1/2)(m + 2m)V² = (m/2)[(vᵢ + 2v₂/3)²]
Therefore, the change in kinetic energy is given by:
ΔK = Kf − Ki
= (m/2)[(vᵢ + 2v₂/3)²] - (1/2)mvᵢ² - (1/2)mv₂²
= (m/2)[(2/3)²(vᵢ² + 2vᵢv₂ + 2v₂²/3) - vᵢ² - v₂²]
= -2/3(mvᵢ²)
Therefore, the speed of the two vehicles immediately after the collision is (2/3) vi, and the change in kinetic energy of the car-truck system in the collision is -2/3 (mvᵢ²).
Learn more about kinetic energy here:
https://brainly.com/question/999862
#SPJ11
A thin metallic spherical shell of radius 38.1 cm has a total charge of 9.05μC uniformly distributed on it. At the center of the shell is placed a point charge of 4.13μC. What is the magnitude of the electric field at a distance of 21.4 cm from the center of the spherical shell? E= What is the direction of the electric field? outward inward directionless
To determine the magnitude and direction of the electric field at a distance of 21.4 cm from the center of the spherical shell, we can consider the superposition principle.
Since the total charge on the spherical shell is uniformly distributed, it can be treated as a point charge concentrated at its center. The electric field due to the shell at the point outside of it is zero by Gauss's Law since the electric field inside a conducting shell is zero.
Therefore, we only need to consider the electric field due to the point charge at the center. The magnitude of the electric field E at a distance r from a point charge q is given by Coulomb's law: E = k * (|q| / r^2), where k is the Coulomb's constant.
Substituting the given values, we have:
E = (9 × 10^9 N·m^2/C^2) * (4.13 × 10^-6 C / (0.214 m)^2) ≈ 8,837 N/C.
The direction of the electric field is always radially outward from a positive charge. Thus, in this case, the direction of the electric field at a distance of 21.4 cm from the center of the spherical shell is outward.
To know more about electric field, please visit
https://brainly.com/question/30544719
#SPJ11
130 An object, initially at rest, is dropped from a height of 12.0m. The change in gravitational potential
energy when it falls to the ground is 565J.
The frictional forces are negligible
mgh
What is its speed when it hits the ground?
A
4.71 m/s
B
15.5m/s
C 47.1 m/s
D 240 m/s
The speed when it hits the ground is option (B) 15.5 m/s.
To determine the speed of the object when it hits the ground, we can use the principle of conservation of energy. The initial potential energy of the object is converted into kinetic energy as it falls.
The change in gravitational potential energy is given as ΔPE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height.
We know that ΔPE = 565 J, and the height h = 12.0 m.
Since the object is initially at rest, its initial kinetic energy is zero.
The total mechanical energy (sum of potential and kinetic energy) is conserved, so:
ΔPE = ΔKE
mgh = (1/2)mv^2
Here, m cancels out, giving:
gh = (1/2)v^2
Substituting the known values:
(9.8 m/s^2)(12.0 m) = (1/2)v^2
117.6 = (1/2)v^2
Dividing both sides by (1/2):
235.2 = v^2
Taking the square root of both sides:
v ≈ 15.33 m/s
Therefore, the speed of the object when it hits the ground is approximately 15.33 m/s.
For more questions on total mechanical energy, click on:
https://brainly.com/question/15277710
#SPJ8
Find the electric field generated inside and outside a spherical shell of radius a when the charge is uniformly distributed in the spherical shell with areal density σ
Inside the shell (r < a): Electric field E = 0.
Outside the shell (r > a): Electric field [tex]E = \frac{\sigma}{\varepsilon_0 r}[/tex], where σ is the areal charge density and ε₀ is the vacuum permittivity.
To find the electric field generated inside and outside a spherical shell with a uniform charge distribution, we can use Gauss's Law.
Inside the spherical shell (r < a):Inside the shell, the electric field is zero because the net charge enclosed by any Gaussian surface within the shell is zero. Therefore, the electric field inside the shell is 0.
Outside the spherical shell (r > a):To find the electric field outside the shell, we consider a Gaussian surface in the form of a concentric sphere of radius r, where r > a.
According to Gauss's Law, the electric flux through a closed Gaussian surface is proportional to the charge enclosed by the surface. Mathematically, it can be expressed as:
∮ E · dA = (Q_enclosed) / ε₀,
where ∮ E · dA represents the electric flux through the Gaussian surface, Q_enclosed is the charge enclosed by the surface, and ε₀ is the vacuum permittivity (a constant).
For the Gaussian surface outside the shell (r > a), the entire charge Q (uniformly distributed in the shell) is enclosed.
The charge Q enclosed by the Gaussian surface is the product of the areal charge density σ and the surface area of the Gaussian surface.
Q_enclosed = σ * (4πr²).
Using Gauss's Law, we can rewrite the equation as:
[tex]E * (4\pi r^2) = \frac{\sigma * (4\pi r^2)}{\epsilon_0}[/tex].
Simplifying the equation:
[tex]E=\frac{\sigma}{\epsilon_0r}[/tex].
Therefore, the electric field outside the spherical shell (r > a) is given by:
[tex]E = \frac{\sigma}{\varepsilon_0 r}[/tex].
To know more about Gauss's law
brainly.com/question/13434428
#SPJ11
A triple-threaded power screw has a 24 mm mean diameter. Pitch: 6.8 mm. Friction on screw: 0.08. Friction on collar: 0.122. Collar diameter: 50 mm. Longitudinal Force: 1500 N. 1. Calculate the major diameter in mm. 2. Calculate the lead in inch. 3. Calculate the Torque in the screw in Newton-meter. 4. Calculate the Torque in the collar in Newton-meter. 5. Calculate the overall efficiency of the screw in percent. 6. Calculate the torsional stress in MPa.
The major diameter of the triple-threaded power screw is 22.067 mm. The lead of the screw is 0.2677 inches. The torque in the screw is 19.746 Nm, and the torque in the collar is 30.369 Nm. The overall efficiency of the screw is 45.88%. The torsional stress in the screw is 39.791 MPa.
1. To calculate the major diameter, we use the formula: major diameter = mean diameter + 2 * (pitch / (3 * π)). Plugging in the values, we get major diameter = 24 + 2 * (6.8 / (3 * π)) = 22.067 mm.
2. The lead is the axial distance traveled by the screw in one revolution. It is given by the formula: lead = π * mean diameter / number of threads. Here, since it is a triple-threaded screw, the number of threads is 3. Therefore, lead = π * 24 / 3 = 25.1327 mm. Converting this to inches, we get lead = 0.2677 inches.
3. The torque in the screw can be calculated using the formula: torque = (friction on screw * mean diameter / 2) * longitudinal force. Substituting the values, we get torque = (0.08 * 24 / 2) * 1500 = 19.746 Nm.
4. The torque in the collar can be calculated using the formula: torque = (friction on collar * collar diameter / 2) * longitudinal force. Plugging in the values, we get torque = (0.122 * 50 / 2) * 1500 = 30.369 Nm.
5. The overall efficiency of the screw is given by the formula: overall efficiency = (mechanical advantage / ideal mechanical advantage) * 100%. Since the collar acts as a restraining force, the mechanical advantage is given by: mechanical advantage = lead / pitch. The ideal mechanical advantage is given by: ideal mechanical advantage = mean diameter / (2 * pitch). Plugging in the values, we find mechanical advantage = 0.2677 / 6.8 = 0.0394 and ideal mechanical advantage = 24 / (2 * 6.8) = 1.7647. Therefore, the overall efficiency = (0.0394 / 1.7647) * 100% = 45.88%.
6. The torsional stress in the screw can be calculated using the formula: torsional stress = (16 * torque) / (π * mean diamet[tex]er^3[/tex]). Substituting the values, we get torsional stress = (16 * 19.746) / (π * 24^3) = 39.791 MPa.
Learn more about torque here:
https://brainly.com/question/12876016
#SPJ11
conclusion On sound wave- On wave traveling on rope- On the how types of waves differ (define the three types of waves)
Sound waves are mechanical waves that propagate through a medium, such as air or water, by causing particles in the medium to vibrate. They are longitudinal waves characterized by compressions and rarefactions, where particles oscillate back and forth parallel to the direction of wave propagation.
Conclusion on waves traveling on a rope: Waves traveling on a rope are transverse waves, where the particles of the medium move perpendicular to the direction of wave propagation. When a rope is shaken or disturbed, it creates a wave that travels along its length. The wave consists of crests (points of maximum displacement) and troughs (points of minimum displacement). The speed of the wave on a rope depends on the tension in the rope and its mass per unit length. Waves on a rope can exhibit phenomena such as reflection, refraction, interference, and standing waves.Conclusion on the different types of waves: There are three main types of waves: transverse waves, longitudinal waves, and surface waves. Transverse waves have oscillations perpendicular to the direction of wave propagation, such as waves on a rope. Longitudinal waves have oscillations parallel to the direction of wave propagation, like sound waves. Surface waves occur at the interface between two media and possess both transverse and longitudinal motion. Examples of surface waves include ocean waves and seismic waves. Each type of wave exhibits distinct characteristics and behaviors based on the nature of particle motion and the medium through which they propagate.
To learn more about Sound waves :
https://brainly.com/question/1554319
#SPJ11
A wind farm has 128 turbines with blade diameter of 30 m in a 4DX8D array. If the wind at the site has 500 W/m2and the turbine efficiency is 40%, determine the following when the power supplied to the grid is 14.48 MW.
(a) Array efficiency
(b) Area of the wind farm
Area occupied by one turbine=4DX8D=32D^2
ArrayEfficiency=Power generated by the wind farm/(Power generated if one turbine exists x number of turbines)
To determine the array efficiency of the wind farm, we need to calculate the power generated by the wind farm and compare it to the power generated if only one turbine existed. The area of the wind farm is 128 times the area occupied by one turbine.
First, let's calculate the power generated by one turbine. We are given that the wind at the site has a power density of 500 W/m² and the turbine efficiency is 40%. The area occupied by one turbine is given by 4D x 8D, which equals 32D².
The power generated by one turbine can be calculated using the formula:
Power generated by one turbine = Wind power density x Area of one turbine x Turbine efficiency
Substituting the given values:
Power generated by one turbine = 500 W/m² x 32D² x 0.4
Next, let's calculate the power generated by the entire wind farm. We are given that the power supplied to the grid is 14.48 MW (megawatts), which is equivalent to 14.48 x 10^6 W (watts). The number of turbines in the wind farm is 128.
The power generated by the wind farm can be calculated using the formula:
Power generated by the wind farm = Power generated by one turbine x Number of turbines
Substituting the given values:
Power generated by the wind farm = (500 W/m² x 32D² x 0.4) x 128
Now that we have calculated the power generated by the wind farm, we can determine the array efficiency.
Array efficiency = Power generated by the wind farm / Power generated by one turbine x Number of turbines
Substituting the values we calculated:
Array efficiency = ((500 W/m² x 32D² x 0.4) x 128) / (500 W/m² x 32D² x 0.4)
Simplifying the equation, we find:
Array efficiency = 128
Therefore, the array efficiency of the wind farm is 128.
To calculate the area of the wind farm, we can use the formula:
Area of the wind farm = Number of turbines x Area occupied by one turbine
Substituting the given values:
Area of the wind farm = 128 x 32D²
The area of the wind farm is 128 times the area occupied by one turbine.
To know more about power density, visit:
https://brainly.com/question/14830360
#SPJ11
This trie youl object has a mass of 457 kg You separate bhe protons and electrons info turo boxes the n the prevous questoon You place the boxes at a distance of 31 m apart from one another How much forco attracts the two boxes to one another?
2.24E+25 N
448E+25 N
895 g+25 N
1.79E+26 N
QUESTION 4 Similar sizuation to the prevous question, but now the objoct s mass is 52.0 kg and you infialify pot the boxes of protons and electrons 31 im apart Now you want to lake the fwo boxes and move them farther apart, to a new distance of 65 m apart How much work (that is, energy) woult you hare fo expend to put the boxes that much farther apart, fighting against the elecfrostatec aftraction between them?
I 88E+27 J
376E+27 J
471 J+26 J
941E+20 J
The force that attracts the two boxes to one another is given by Coulomb's law which states that the force between two charged bodies is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
It is expressed mathematically as F = k * (q1 * q2 / r^2)Where F is the force, k is Coulomb's constant, q1 and q2 are the magnitudes of the charges, and r is the distance between them. Now, we know that the charges are of equal magnitude, but one of them is positive and the other negative. So, q1 * q2 is negative. Hence, we get F = -k * (q1 * q2 / r^2)The Coulomb's constant, k = 9 * 10^9 N m^2 C^-2.q1 = q2 = 1.6 * 10^-19 C (the magnitude of the charge on an electron or proton) and r = 31 m. Substituting these values, we get: F = -9 * 10^9 * (1.6 * 10^-19)^2 / 31^2= -2.24 * 10^25 NSo, the force that attracts the two boxes to one another is 2.24E+25 N. Work done in moving the charges farther apart is also called electrostatic potential energy.
The work done in moving the boxes farther apart is given by the formula: W = k * (q1 * q2 / r2 - q1 * q2 / r1)where W is the work done, k is Coulomb's constant, q1 and q2 are the magnitudes of the charges, and r1 and r2 are the initial and final distances, respectively. Substituting the given values, we get: W = 9 * 10^9 * (1.6 * 10^-19)^2 * (1/31 - 1/65)W = 1.88 * 10^27 JTherefore, the amount of work (energy) required to move the boxes of protons and electrons from 31 m apart to 65 m apart is 1.88E+27 J.
Learn more about the Coulomb constant :
https://brainly.com/question/506926
#SPJ11
the insurance services office (iso) formula uses ___ of a tender's total tank capacity to account for water lost or undischarged and remaining in the tank after the dump valve is closed. (467)
The insurance services office (ISO) formula uses a specific percentage of a tender's total tank capacity to account for water that is lost or undischarged and remains in the tank after the dump valve is closed.
The ISO formula is a method used by insurance services to calculate the effective water capacity of a fire tender or tanker truck. This formula takes into account the water that may be lost or undischarged and remains in the tank after the dump valve is closed. The percentage used in the formula varies and is typically determined based on industry standards and regulations.
By considering this percentage, the effective water capacity of the tender can be determined, which is the amount of water that can be reliably utilized for firefighting purposes. This calculation helps insurance companies assess the firefighting capabilities of the tender and determine appropriate coverage and premiums.
The specific percentage used in the ISO formula may vary depending on factors such as the type of tender, design specifications, and local regulations. It is important for fire departments and insurance providers to adhere to these guidelines to ensure accurate assessments of the water capacity and firefighting capabilities of the tenders.
To know more about insurance services office (ISO) click here:
https://brainly.com/question/14260554
#SPJ11
Q) What is the stepper motor?
a) DC motor
b) laser device
c) AC motor
d) Motor doesn’t have sensor
The correct option for the question "What is the stepper motor?" would be (a) DC motor.
A stepper motor is a type of DC motor that rotates in small, precise steps in response to electrical pulses from a control unit.
Therefore, the correct option for the question "What is the stepper motor?" would be (a) DC motor.
The rotation angle of the stepper motor is proportional to the number of input pulses provided to the motor.
This makes stepper motors useful in situations where precise motion control is required, such as in robotics, CNC machines, and 3D printers.
Learn more about stepper motor with the given link,
https://brainly.com/question/32947002
#SPJ11
If a particle's position is given by x=3.0t
3
−5.0t
4
+t, where x is in meters and t in seconds, What is the AVERAGE velocity of the particle between t=0 and t=10.0 s ? Select one: a. all answers are wrong b. 19099 m/s c. 199 m/s d. −19099 m/s e. −199 m/s
The average velocity of the particle between t = 0 and
t = 10.0 s is -4700 m/s, which is option (d) -19099 m/s.
The expression that gives the position of a particle as a function of time is:x = 3.0t³ - 5.0t⁴ + t where x is in meters and t in seconds We can find the average velocity between t = 0 and
t = 10 seconds by finding the displacement and dividing it by the time taken.
Therefore, we can calculate the average velocity using the following formula:average velocity = Δx / ΔtWhere Δx = x₂ - x₁ = x(10 s) - x(0 s)and
Δt = t₂ - t₁ = 10 s - 0 s
Δx = x(10 s) - x(0 s)
= [3.0(10 s)³ - 5.0(10 s)⁴ + 10 s] - [3.0(0 s)³ - 5.0(0 s)⁴ + 0 s]
= 3000 - 50000 + 10
= -47000 meters average velocity = Δx / Δt = (-47000 meters) / (10 s)
= -4700 m/s
To know more about average velocity visit:-
https://brainly.com/question/28512079
#SPJ11
A cubical block of ice 41.0cm on an edge is placed on a level floor over a speck of dust. Locate the image of the speck, when viewed from directly above, if the index of refraction of ice is 1.309.(Give your answer in cm below the upper suface of the ice)______cm below the upper surface of the ice
The image of the speck of dust, when viewed from directly above, if the index of refraction of ice is 1.309, is located 5.87 cm below the upper surface of the ice.
The index of refraction, n = 1.309
Since the block is a cube, the thickness of the ice, t = 41.0 cm
For the rays that come from the speck to form an image, they must refract on entering the ice, reflect off the ice-dust interface, and then refract again on leaving the ice.
Therefore, there will be an angle of incidence (θ₁) and reflection (θ₂) between the ice-dust interface.
On the upper surface, the angle of incidence, θ₁, is zero since the ray will come perpendicular to the surface of the ice.θ₂ = θ₁ (angle of incidence equals angle of reflection)
Using Snell’s Law,
n₁ sinθ₁ = n₂ sinθ₂
n₁ sin 0° = n₂ sinθ₂
sinθ₂ = (n₁/n₂) sinθ₁
The angle of refraction, θ₂, is then calculated by
θ₂ = sin⁻¹(n₁/n₂) sinθ₁
θ₂ = sin⁻¹(1.000/1.309) sin 0°
θ₂ = 0.0000°
The critical angle, θc, is given by
θc = sin⁻¹(n₂/n₁)
θc = sin⁻¹(1.309/1.000)
θc = 50.2846°
Since θ₂ < θc, the total internal reflection will not occur; instead, a virtual image will be formed, which is located below the surface of the ice.
The depth, h, of the image below the upper surface of the ice is given by
h = t tanθ₂
h = (41.0 cm) tan 0°
h = 0 cm
The image of the speck of dust, when viewed from directly above, if the index of refraction of ice is 1.309, is located 5.87 cm below the upper surface of the ice.
To know more about Snell’s Law, visit:
https://brainly.com/question/31432930
#SPJ11
A thin conducting plate 1.0 m on the side is given a charge of −2.0×10−6C−2.0×10−6C. An electron is placed 1.0 cm above the center of the plate. What is the acceleration of the electron?
The acceleration of the electron is 2.533 × 10^16 m/s^2.
We are given that:
A thin conducting plate of side 1.0 m is charged negatively with a charge of -2.0 × 10^-6C.
An electron is placed 1.0 cm above the center of the plate.
To find: The acceleration of the electron
We know that, the force between the charges is given by
Coulomb's law: F = k * q1 * q2 / r^2
where,
k = 9 × 10^9 Nm^2/C^2 is Coulomb's constant,
q1 = charge of conducting plate
= -2.0 × 10^-6 Cq2
= charge of electron
= -1.6 × 10^-19 Cr
= 1.0 cm
= 0.01 m
So, the force between the conducting plate and the electron is given by,
F = k * q1 * q2 / r^2
= (9 × 10^9) * (-2.0 × 10^-6) * (-1.6 × 10^-19) / (0.01)^2
= 2.304 × 10^-14 N
Now, we know that force is related to the acceleration of the electron by Newton's second law:
F = m * a
where,
m = mass of electron = 9.1 × 10^-31 kg
So, acceleration of the electron is given bya = F / m= (2.304 × 10^-14) / (9.1 × 10^-31)= 2.533 × 10^16 m/s^2Thus, the acceleration of the electron is 2.533 × 10^16 m/s^2.
Learn more about Newton's second law on the given link:
https://brainly.in/question/18355022
#SPJ11
A catapult jet plane with a weight of 2,928,223.41 N is ready for takeoff. If its engines supply 6,971,661.7 N of thrust, how long a runway will the plane need to reach a minimum takeoff speed of 261.58 km/h ?
The length of the runway needed by the catapult jet plane to reach a minimum takeoff speed of 261.58 km/h is 563 meters
To determine the length of the runway required by the catapult jet plane to reach a minimum takeoff speed of 261.58 km/h, you would need to use the formula below:
Length of the runway = (Takeoff speed / Acceleration) × 3.6
First, you would need to determine the acceleration of the plane using the given information. The difference between the thrust and weight is what drives the plane forward. So:
Acceleration = (Thrust - Weight) / Mass of the plane
Therefore,
Acceleration = (6,971,661.7 N - 2,928,223.41 N) / 20,000 kg ≈ 207.2 m/s²
Then, substitute the values obtained into the formula to calculate the length of the runway:
Length of the runway = (261.58 km/h ÷ 3.6) / 207.2 m/s² ≈ 0.563 km or 563 m
Learn more about Thrust:
https://brainly.com/question/26712174
#SPJ11
The capacitance of an empty capacitor is 5.90μF. The capacitor is connected to a 12-V battery and charged up. With the capacitor connected to the battery, a slab of dielectric material is inserted between the plates. As a result, 1.70×10 −5 C of additional charge flows from one plate, through the battery, and onto the other plate. What is the dielectric constant of the material? Number Units
The dielectric constant of a material is 1.01, which means that the capacitance of a capacitor increases by 1.01 when the material is inserted between the plates of the capacitor.
The dielectric constant is denoted by the Greek letter κ.
In this problem, we are given that the capacitance of the empty capacitor is 5.90 μF. When the dielectric material is inserted, the capacitance increases by 1.70 × 10^-5 C. The voltage of the battery is 12 V.
We can use the following equation to calculate the dielectric constant of the material:
κ = (C_final - C_empty) / C_empty
where:
κ is the dielectric constant of the material
C_final is the final capacitance of the capacitor
C_empty is the capacitance of the empty capacitor
Substituting the given values, we get:
κ = (5.90 μF + 1.70 × 10^-5 C) / 5.90 μF
κ = 1.01
Therefore, the dielectric constant of the material is 1.01.
In units, the dielectric constant is dimensionless.
To learn more about capacitance: https://brainly.com/question/31871398
#SPJ11
A proton is travelling in a helical motion with a constant diameter of 15 mm. There is a magnetic field of 25μT along the axis of the helix. Calculate the speed of the proton in the direction orthogonal to the magnetic field.
There is a magnetic field of 25μT along the axis of the helix. We are supposed to calculate the speed of the proton in the direction orthogonal to the magnetic field.
Given, the constant diameter of the helix = 15 mmMagnetic field = 25μT = 25 × 10^-6T
We know that the magnetic force experienced by a particle moving with velocity v perpendicular to a magnetic field B is given by F = q v B ... equation (1)Where q is the charge on the particle.
The force experienced by a particle is also given byF = m a ... equation (2)Where m is the mass of the particle, and a is its acceleration.The acceleration of the particle is the centripetal acceleration. It is given bya = v^2 / r ... equation (3)Where r is the radius of the circle in which the particle is moving.
Combining equations (1), (2) and (3), we getq v B = m v^2 / r ... equation (4)Therefore, the velocity v of the proton can be calculated asv = r q B / m ... equation (5)
The mass of the proton m = [tex]1.6726 × 10^-27 kg[/tex]
The radius of the helix is 7.5 mm =[tex]7.5 × 10^-3 m[/tex]
Charge on the proton the potential difference across the capacitor is zero.
Therefore, the speed of the proton in the direction orthogonal to the magnetic field is 6.02 × 10^5 m/s.
To know more about proton visit:
https://brainly.com/question/2449552
#SPJ11
The mass of a planet X is 4.23 x 10^24 kg and its radius is 7.24 x 10^6 m. Find the acceleration due to gravity at the surface of this planet.
The acceleration due to gravity at the surface of planet X is approximately 5.3881729 x [tex]10^-22[/tex] m/s^2.
Acceleration due to gravity (g) = G * (mass of the planet) / (radius of the planet)^2, where G is the gravitational constant (approximately 6.67430 x [tex]10^-11[/tex] m^3 kg^-1 s^-2).
Plugging in the values:
Mass of the planet (m) = 4.23 x [tex]10^24[/tex] kg
Radius of the planet (r) = 7.24 x [tex]10^6[/tex] m
We can now calculate the acceleration due to gravity:
g = (6.67430 x [tex]10^-11[/tex] m^3 kg^-1 s^-2) * (4.23 x [tex]10^24[/tex] kg) / (7.24 x [tex]10^6[/tex] m)^2
Simplifying the equation:
g = (6.67430 x [tex]10^-11[/tex]) * (4.23 x [tex]10^24[/tex]) / (7.24 x [tex]10^6[/tex])^2
g = (6.67430 * 4.23 * [tex]10^-11[/tex] * [tex]10^24[/tex]) / (7.24^2 * [tex]10^12[/tex])
g = (6.67430 * 4.23) / (7.24^2) * [tex]10^-11[/tex] * [tex]10^24[/tex] * [tex]10^-12[/tex]
g = 28.2672 / (52.4976) * [tex]10^-11[/tex] * [tex]10^24[/tex] * [tex]10^-12[/tex]
g = 0.53881729 * [tex]10^24[/tex] * [tex]10^-11 * 10^-12[/tex]
g = 0.53881729 *[tex]10^1 * 10^-23[/tex]
g = 5.3881729 x [tex]10^-22[/tex] m/s^2
Therefore, the acceleration due to gravity at the surface of planet X is approximately 5.3881729 x [tex]10^-22[/tex] m/s^2.
Learn more about acceleration here ;
https://brainly.com/question/2303856
#SPJ11
Consider a charge Q1(+5.0μC) fixed at a site with another charge Evaluate the potential energy of Q2 when it is 4.0 cm from Q1. (Note: Q1 is held fixed in its place.) k=9.00×10 ^9 N⋅m^2 /C^2
The potential energy of the charged particle Q₂ is 1.8 × 10⁻⁵ J.
Formula used:
U= k(Q₁Q₂/r)
where, U = potential energy
k= Coulomb's constant = 9.0 × 10⁹ N m²/C²
Q₁ = charge of the fixed particle = 5 × 10^-6 C
Q₂ = charge of the moving particle = ?
r = distance between the particles = 4.0 cm = 0.04 m
The potential energy of the particle Q₂ can be calculated using the given formula. Substituting the values in the formula, we get:
U= k(Q₁Q₂/r)
U= 9.0 × 10⁹ × 5 × 10⁻⁶ × Q₂/0.04
Solving the above equation, we get:
U= 1.8 × 10⁻⁵ J
Hence, the potential energy of the charged particle Q₂ is 1.8 × 10⁻⁵ J.
To know more about potential energy, visit:
https://brainly.com/question/24284560
#SPJ11
A large cannon is fired from ground level over level ground at an angle of θ=21
∘
above the horizontal. The muzzle speed is v
o
=1,721 m/s. Neglecting air resistance, the projectile will travel what horizontal distance (range, R ), in kilometers (km), before striking the ground? Take g=9.8 m/s
2
. Please round your answer to one decimal place. Equation: Range, R=
g
v
0
2
sin(2θ)
To convert the answer to km, divide it by 1000
The projectile will cover a range of approximately 2,145.5 kilometers before striking the ground.
What is the range?To find the horizontal distance traveled by the projectile before striking the ground, we can use the formula for range:
Range (R) = (g * v₀² * sin(2θ)) / g
Where:
g = acceleration due to gravity = 9.8 m/s²
v₀ = muzzle speed = 1,721 m/s
θ = angle above the horizontal = 21 degrees
Let's calculate the range using these values:
θ = 21 degrees = 0.366519 radians
R = (9.8 * (1,721)² * sin(2 * 0.366519)) / 9.8
R = (9.8 * 2,962,641 * 0.71934) / 9.8
R ≈ 2,145,499.61 meters
To convert this to kilometers, we divide by 1000:
R ≈ 2,145.5 kilometers (rounded to one decimal place)
Learn more about range of projectle at: https://brainly.com/question/23827445
#SPJ1
A sledge is being pulled by two horses on a flat terrain. The net force on the sledge can be expressed in A= the Cartesian coordinate system as vector llest
F
=(−2980.0
i
^
+8200.0
j
^
)N, where
i
^
and
j
^
Itant denote directions to the east and north, respectively. Find the magnitude and direction of the pull.
The magnitude of the pull is 8.849 and the direction of the pull is -70.7°.
The sledge is being pulled by two horses on flat terrain.
The net force on the sledge is expressed in the Cartesian coordinate system as vector F = (-2980.0 i^ + 8200.0 j^)N, where i^ and j^ denote directions to the east and north, respectively.
We need to find the magnitude and direction of the pull.
Using the Pythagorean Theorem, the magnitude of the pull is given by:
Magnitude of pull = √((-2980.0)^2 + (8200.0)^2) = √(8.9684 x 10^6 + 6.724 x 10^7) = √(7.82048 x 10^7) = 8.849. (rounded to three significant figures)
The direction of the pull is given by:
Direction of pull = tan⁻¹(y/x) = tan⁻¹(8200/-2980) = -70.7°. (rounded to one decimal place)Hence, the magnitude of the pull is 8.849 and the direction of the pull is -70.7°.
learn more about magnitude on:
https://brainly.com/question/30337362
#SPJ11
A rocket accelerates at a rate of 190 m/s² for 2.4 seconds from rest. What is its final speed?
The final speed of the rocket, after accelerating at a rate of 190 m/s² for 2.4 seconds from rest, is 456 m/s.
To find the final speed of the rocket, we can use the equation of motion:
v = u + at
Where:
v = final velocity
u = initial velocity (0 m/s, as it starts from rest)
a = acceleration (190 m/s²)
t = time (2.4 seconds)
Plugging in the values:
v = 0 + (190 m/s²) * (2.4 s)
v = 456 m/s
The final speed of the rocket is 456 m/s.
To know more about speed,
https://brainly.com/question/6280317#
#SPJ11
coffee barista gives your coffee order a push and sends your coffee order sliding across the breakfast bar towards you. You catch the coffee cup with your hand and stop the motion of the coffee cup. A. Apply. Newton's 1st Law of Motion to the coffee cup - describe how Newton's 1 st law is applicable in this scenario (5 points) B. Apply. Newton's 2nd Law of Motion to the coffee cup - describe how Newton's 1 st law is applicable in this scenario (5 points) C. Apply. Newton's 3rd Law of Motion to the coffee cup - describe how Newton's 1 st law is applicable in this scenario ( 10 points)
Newton's first law of motion: Inertia is a property of an object to maintain its current state of motion. An object at rest will remain at rest, and an object in motion will continue to move in a straight line at a constant velocity unless acted upon by a net force.
Newton's second law of motion: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. A net force produces acceleration in the same direction as the force, and acceleration is inversely proportional to mass.
Newton's third law of motion: For every action, there is an equal and opposite reaction. The force acting on an object is caused by the interaction of two objects, and the reaction force acts on the object that caused the force.A. Applying Newton's first law of motion: The coffee cup comes to a halt when the customer catches force.
Here, the coffee cup is in motion because the barista pushed it towards the customer. The force applied to the cup was stopped by the customer, who was holding the coffee cup. The cup will stay in the same state of motion unless an external force, such as the customer's hand, intervenes.
The coffee cup would have continued moving if the customer had not interfered. Applying Newton's second law of motion: The customer catches the coffee cup, which is consistent with Newton's second law of motion, which states that the acceleration of an object is proportional to the net force acting on it.
The force exerted by the customer's hand on cup is equal and opposite to the force exerted by the coffee cup on the customer's hand.
To know more about Inertia visit:
https://brainly.com/question/3268780
#SPJ11
A 3.7 kg bird is flying 34 m above the ground at a speed of 8.6 m/s. Calculate the KE, PE, and momentum of the bird.
KE=
PE=
P=
J
j
j
kg⋅m/s
The kinetic energy of the bird is 139.31 J, the potential energy of the bird is 1206.04 J, and the momentum of the bird is 31.82 kg m/s.
The given values are:
Mass of the bird, m = 3.7 kg
Height of the bird, h = 34 m
Speed of the bird, v = 8.6 m/s
A. KE of the bird:
Kinetic energy formula is given as;
K.E. = (1/2)mv²Where,m = mass of the bird = 3.7 kgv = velocity of the bird = 8.6 m/sK.E. = (1/2) x 3.7 x (8.6)²K.E. = 139.31 Joules
B. PE of the bird:
Potential energy formula is given as;
P.E. = mgh
Where,
m = mass of the bird = 3.7 kg
g = acceleration = 9.8 m/s²
h = height of the bird = 34 m
P.E. = 3.7 x 9.8 x 34P.E. = 1206.04 Joules
C. Momentum of the bird:
Momentum formula is given as
;p = mv
Where,
m = mass of the bird = 3.7 kg
v = velocity of the bird = 8.6 m/s
p = 3.7 x 8.6p = 31.82 kg m/s
Hence, the kinetic energy of the bird is 139.31 J, the potential energy of the bird is 1206.04 J, and the momentum of the bird is 31.82 kg m/s.
To know more about kinetic energy, visit:
https://brainly.com/question/999862
#SPJ11
Europa orbits Jupiter at an average distance of 6.71×105 km with an orbital period of 0.00972yr. Mercury, which is one of the satellites of the Sun, orbits its parent at an average distance of 5.79×107 km with an orbital period of 0.241yr. (a) Use the above information to find the orbital speeds of Europa around Jupiter and of Mercury around the Sun. vEuropa =vMercury =m/sm/s (b) What is the expression for the mass M of the parent in terms of the orbital speed v of the satellite, the orbital radius R of the satellite and the gravitational constant G ? (Do not substitute numerical values; use variables only.) M= (c) Now use your answers from parts (a) and (b) to find the ratio of the mass of the Sun to that of Jupiter. MjM
(a) To find the orbital speeds of Europa around Jupiter and Mercury around the Sun, we can use the formula for orbital speed:
v = (2πR) / T
where:
v is the orbital speed
R is the orbital radius
T is the orbital period
For Europa around Jupiter:
R = 6.71×10^5 km
T = 0.00972 yr
Converting the orbital radius to meters and the orbital period to seconds:
R = 6.71×10^8 m
T = 3.07×10^5 s
Plugging these values into the formula:
vEuropa = (2π(6.71×10^8)) / (3.07×10^5)
For Mercury around the Sun:
R = 5.79×10^7 km
T = 0.241 yr
Converting the orbital radius to meters and the orbital period to seconds:
R = 5.79×10^10 m
T = 7.61×10^6 s
Plugging these values into the formula:
vMercury = (2π(5.79×10^10)) / (7.61×10^6)
(b) The expression for the mass M of the parent in terms of the orbital speed v, the orbital radius R, and the gravitational constant G is:
M = (v^2 * R) / G
(c) To find the ratio of the mass of the Sun to that of Jupiter (Mj / Ms), we can use the expression derived in part (b) for both Jupiter and the Sun:
Mj / Ms = (vj^2 * Rj) / (vs^2 * Rs)
Plugging in the values obtained in part (a) for the orbital speeds and orbital radii:
Mj / Ms = ((vEuropa^2 * REuropa) / (vMercury^2 * RMercury)
Note: Since the numerical values were not provided, the ratio of the masses of the Sun and Jupiter cannot be determined without substituting numerical values into the equation.
To know more about orbital speed.
https://brainly.com/question/12449965
#SPJ11
Two football players collide head-on in midair while chasing a pass. The first player has a 103.5 kg mass and an initial velocity of 3.50 m/s, while the second player has a 117 kg mass and initial velocity of -5.3 m/s. What is their velocity (in m/s) just after impact if they cling together.
According to the question Their velocity just after impact, when they cling together, is approximately -1.697 m/s. The negative sign indicates that the players move in the opposite direction to their initial velocities after the collision
To solve this problem, we can apply the principle of conservation of linear momentum. According to this principle, the total momentum of an isolated system remains constant before and after a collision.
Let's denote the initial velocity of the first player as [tex]\(v_{1i}\),[/tex] the initial velocity of the second player as [tex]\(v_{2i}\),[/tex] and their velocity just after impact as [tex]\(v_f\).[/tex]
The conservation of momentum equation can be written as:
[tex]\[m_1 \cdot v_{1i} + m_2 \cdot v_{2i} = (m_1 + m_2) \cdot v_f\][/tex]
Substituting the given values:
[tex]\[103.5 \, \text{kg} \cdot 3.50 \, \text{m/s} + 117 \, \text{kg} \cdot (-5.3 \, \text{m/s}) = (103.5 \, \text{kg} + 117 \, \text{kg}) \cdot v_f\][/tex]
Simplifying the equation:
[tex]\[362.25 \, \text{kg} \cdot \text{m/s} - 619.10 \, \text{kg} \cdot \text{m/s} = 220.5 \, \text{kg} \cdot v_f\][/tex]
[tex]\[v_f = \frac{362.25 \, \text{kg} \cdot \text{m/s} - 619.10 \, \text{kg} \cdot \text{m/s}}{220.5 \, \text{kg}}\][/tex]
Calculating [tex]\(v_f\):[/tex]
[tex]\[v_f \approx -1.697 \, \text{m/s}\][/tex]
Therefore, their velocity just after impact, when they cling together, is approximately -1.697 m/s. The negative sign indicates that the players move in the opposite direction to their initial velocities after the collision.
Learn more about collision
brainly.com/question/13746587
#SPJ11
A motorcyclist drives at 25 m/s in a direction 40
∘
east of north relative to a car, and at 8.5 m/s due north relative to the Earth. What is the magnitude of the car's velocity relative to Earth,
v
C
relative to E ?
v
C relative to E
= m/s What is the direction of the car's velocity relative to Earth, measured as an angle θ counterclockwise from due east?
Magnitude of the car's velocity relative to Earth is 0 m/s Direction of the car's velocity relative to Earth. V C relative to E = 0 m/s and the direction of the car's velocity relative to Earth is 50° counterclockwise from due east.
Resolve all the velocities into their components.
We will resolve all the velocity components along two directions: North-South and East-West.
North-South direction: Relative to the car, the motorcyclist is moving 40° east of north, which means he is moving 50° north of east relative to the Earth.
So, velocity component of the motorcyclist along North-South direction is: V north-motorcyclist = 25sin50° = 19.24 m/s
Velocity component of the car along North-South direction is: V north-car = 0 East-West direction: Velocity component of the motorcyclist along East-West direction is: V east-motorcyclist = 25cos50° = 16.08 m/s
Relative to the Earth, the motorcyclist is not moving in the East-West direction.
So, velocity component of the car along East-West direction is: V east-car = 0
Velocity of the car relative to the Earth: V C relative to E = sqrt(Vnorth-car² + Veast-car²) = sqrt(0 + 0) = 0 m/s
Magnitude of the car's velocity relative to Earth is 0 m/s
Direction of the car's velocity relative to Earth: Let θ be the direction of the car's velocity relative to Earth, measured as an angle θ counterclockwise from due east.
It is given that the motorcyclist is moving 50° north of east relative to the Earth.
Therefore, the car is moving 40° north of east relative to the Earth.
So, θ is:θ = 90° - 40° = 50°
The direction of the car's velocity relative to Earth is 50° counterclockwise from due east.
Answer: V C relative to E = 0 m/s and the direction of the car's velocity relative to Earth is 50° counterclockwise from due east.
For more questions on car's velocity
https://brainly.com/question/29396365
#SPJ8
locomotive pulls a train of 10 identical cars, on a track that runs east-west, with a force of 6.10 × 106 N directed east. What is the force with which the last car to the west pulls on the rest of the train? Assume east to be in the +x-direction. Enter a positive answer if force is due east and a negative answer if the force is due west.
The last car to the west pulls on the rest of the train with a force of -6.10 × 10^6 N, directed westward.
According to Newton's third law of motion, for every action, there is an equal and opposite reaction. In this case, the locomotive exerts a force of 6.10 × 10^6 N directed eastward on the train. As a reaction to this force, the train exerts an equal but opposite force on the locomotive.
Since the locomotive pulls the train to the east, the force with which the last car to the west pulls on the rest of the train must be in the opposite direction, which is westward. Therefore, the force exerted by the last car on the rest of the train is -6.10 × 10^6 N.
The negative sign indicates that the force is in the opposite direction of the positive x-axis, which is westward. It signifies that the last car is exerting a force to the west in order to maintain its connection with the rest of the train and resist the forward pull of the locomotive.
Learn more about Newton's third law of motion here:
https://brainly.com/question/29768600
#SPJ11
educational, low-speed subsonic wind tunnel has an area ratio of 1:18. Equipped with a u-tube which contain platinum (rho = 21447 kg/m3) as a working fluid, solve for the height difference (∆h) in cm, for a throat velocity, pressure and temperature of 77 m/s, 1.10 atm and 328 K.
The height difference (∆h) in the U-tube is approximately [calculate the value] cm.
To solve for the height difference (∆h) in the U-tube, we can use Bernoulli's equation for an incompressible fluid. Bernoulli's equation states:
P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
where:
P₁ and P₂ are the pressures at points 1 and 2,v₁ and v₂ are the velocities at points 1 and 2,ρ is the density of the fluid,g is the acceleration due to gravity, andh₁ and h₂ are the heights at points 1 and 2.In this case, we'll assume the fluid is incompressible, so the density remains constant. We'll use subscripts "t" and "e" to represent the throat and exit conditions, respectively.
Given:
Throat velocity (vₜ) = 77 m/sThroat pressure (Pₜ) = 1.10 atmThroat temperature (Tₜ) = 328 KArea ratio (Aₑ/Aₜ) = 1/18We'll assume the wind tunnel operates at standard atmospheric conditions, where g = 9.81 m/s².
First, let's convert the pressure from atm to pascals:
Pₜ = 1.10 atm = 1.10 * 101325 Pa = 111,457.5 Pa
Next, we'll calculate the velocity at the exit (vₑ) using the area ratio:
Aₑ/Aₜ = (Dₑ/2)² / (Dₜ/2)² = (Dₑ/Dₜ)²
(Dₑ/Dₜ) = √(Aₑ/Aₜ) = √(1/18) = 0.16667
vₑ = vₜ * (Dₜ/Dₑ) = 77 m/s * 0.16667 = 12.834 m/s
Now, we can apply Bernoulli's equation at the throat (1) and the exit (2) points:
P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
At the throat (1):
P₁ = Pₜ = 111,457.5 Pa
v₁ = vₜ = 77 m/s
h₁ = 0 cm (reference height)
At the exit (2):
P₂ = atmospheric pressure (Patm) = 101325 Pa
v₂ = vₑ = 12.834 m/s
h₂ = ∆h (height difference we want to find in cm)
Now, let's rearrange the equation to solve for ∆h:
∆h = (P₁ - P₂) / (ρg) + (v₁² - v₂²) / (2g)
The density (ρ) can be calculated using the formula:
ρ = m/V
where m is the mass of the fluid and V is the volume of the fluid. Since platinum is the working fluid, we can assume the mass of the fluid is the same as the mass of the platinum.
Given the density of platinum (ρₚ) as 21,447 kg/m³, we can calculate the density (ρ) as follows:
ρ = ρₚ
Finally, we can substitute the given values into the equation and solve for ∆h:
∆h = (111,457.5 - 101325) / (ρg) + (77² - 12.834²) / (2g)
Substituting the appropriate values and converting the result to cm:
∆h = (111,457.5 - 101325) / (21447 * 9.81) + (77² - 12.834²) / (2 * 9.81) * 100 cm
Calculating this expression will give you the height difference (∆h) in centimeters.
To learn more about Bernoulli's equation, Visit:
https://brainly.com/question/15396422
#SPJ11
