The function h(0) = -16t2 + vt + 10 gives the height of a platform diver above the water, in feet, t seconds after

Complete Question:

The height of a diver jumping from a diving platform is about [tex]h(t)= 16t^2 +11t+10[/tex], where h is the height of the diver in feet above the water and t is the time measured in seconds, when diving from a platform about 34.3 feet above the water with an upward initial velocity of 11 ft/sec..  After how many seconds is the diver's height above the water 15 feet?

Answer:

0.3125 seconds

Step-by-step explanation:

Given

[tex]h(t)= 16t^2 +11t+10[/tex]

Required

Time when the diver is above 15ft

This implies that h(t) = 15

So, we have:

[tex]15= 16t^2 +11t+10[/tex]

Collect Like Terms

[tex]0= 16t^2 +11t+10 - 15[/tex]

[tex]0= 16t^2 +11t-5[/tex]

[tex]16t^2 +11t-5=0[/tex]

Expand:

[tex]16t^2 + 16t - 5t - 5 = 0[/tex]

Factorize:

[tex]16t(t + 1) - 5(t + 1) = 0[/tex]

[tex](16t - 5)(t + 1)=0[/tex]

Split

[tex]16t - 5 = 0[/tex] or [tex]t + 1 = 0[/tex]

[tex]16t = 5[/tex] or [tex]t + 1 = 0[/tex]

Solve for t

[tex]t = 5/16[/tex] or [tex]t = -1[/tex]

[tex]t = 0.3125[/tex] or [tex]t = -1[/tex]

But time can't be negative. So:

[tex]t = 0.3125[/tex]

Hence, it will take the diver 0.3125 seconds to be at a height above 15 feet

It will take t = 0.3125 seconds is the diver's height above the water 15 feet.

Given ,

The height of a diver jumping from a diving platform is h

 h(t) = [tex]-16t^{2} + vt + 10[/tex]

The diver's height above the water 15 feet

Velocity = v = 11 ft per second

We have to find, t seconds is the diver's height above the water 15 feet.

According to the question,

[tex]h(t) = -16t^{2} +vt+10[/tex]

Where v = 11, h(t) = 15

15 = -16[tex]t^{2}[/tex] + 11t + 10  

15 - 10 = [tex]-16t^{2} + 11t[/tex]

5 = [tex]-16t^{2} +11t[/tex]

[tex]16t^{2} -11t +5= 0[/tex]

[tex]16t^{2} -16t - 5t + 5 = 0[/tex]

16t ( t - 1 ) - 5 ( t + 1 ) = 0

(16t - 5 ) ( t + 1 ) = 0

16t - 5 = 0

16t = 5

t = [tex]\frac{5}{16}[/tex]

t = 0.3125

And t + 1 = 0

t = -1

Time can not be negative so we can't take t = -1 .

So, The required value of time is t = 0.3125

Hence, it will take t= 0.3125 seconds is the diver's height above the water 15 feet.

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