A 92.45 kg baseball player slides to a stop at third base. The coefficient of kinetic friction between the player and the ground is
0.68. Her speed at the start of the slide is 6.87 m/s.
(a) Calculate her acceleration during the slide.
(b) How long (in time) does she slide until she stops?

Answers

Answer 1

a) Her acceleration during the slide is -6.67 m/s².

b) She slides 1.03 seconds until she stops.

a) We can find her acceleration during the slide with Newton's second law:

[tex] F = ma [/tex]                        

Where:

F: is the force    

m: is the mass = 92.45 kg

a: is the acceleration =?

The force acting on the baseball player is equal to the friction force ([tex]F_{\mu}[/tex]), and it is negative because it is in the opposite direction to the motion:

[tex] -\mu N = ma [/tex]

[tex] -\mu mg = ma [/tex]

[tex] a = -\mu g [/tex]

Where:

N: is the normal force = mg

μ: is the coefficient of kinetic firction = 0.68

g: is the acceleration due to gravity = 9.81 m/s²

Hence, her acceleration during the slide is:

[tex] a = -0.68*9.81 m/s^{2} = -6.67 m/s^{2} [/tex]

b) We can calculate how long does she slide until she stops with the following kinematic equation:

[tex] v_{f} = v_{0} + at [/tex]

Where:

[tex] v_{f} [/tex]: is the final speed = 0 (when she stops)

[tex] v_{0} [/tex]: is the initial speed = 6.87 m/s

t: is the time =?

Then, the time is:

[tex] t = -\frac{v_{0}}{a} = -\frac{6.87 m/s}{-6.67 m/s^{2}} = 1.03 s [/tex]

You can learn more about Newton's second law here: https://brainly.com/question/19860811?referrer=searchResults

I hope it helps you!


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