Serena Williams consistently serves a tennis ball with a top speed of 128 mph. The ball is accelerated essentially from rest (assume v0 = 0 mph) to top speed while it is in contact with the racket for 5 milliseconds. LaTeX: a=\frac{\left(vf-vo\right)}{t}a = ( v f − v o ) t Where a is the acceleration, vf is the final (top) velocity, v0 is the initial velocity, and t is time. If the mass of the average tennis ball is 5.85 g, what force must Serena exert on the ball during that time to achieve the required acceleration, in units of Newtons?

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mavila18 mavila18 · Answer 1 · 2020-05-17T03:05:17+02:00

Answer:

66.94N

Explanation:

To find the force you use the second Newton law, which is given by:

[tex]F=ma[/tex] (1)

m: mass of the ball 5.85g

the acceleration is:

[tex]a=\frac{v_f-v_o}{t}[/tex]

vf: final velocity = 128mph = 57.21m/s

vo : initial velocity = 0m/s

t: time = 5ms =5*10^{-3}s

by computing the acceleration and replacing it in the equation (1) you obtain:

[tex]a=\frac{57.21m/s}{5*10^{-3}s}=11443.2\frac{m}{s^2}\\\\F=(5.85*10^{-3}kg)(11443.20m/s^2)=66.94N[/tex]

hence, the force applied by Serena on the ball is 66.94N