Question

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?

Answer 1

66.94N

Step-by-step explanation:

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

`F=ma` (1)

m: mass of the ball 5.85g

the acceleration is:

`a=(v_f-v_o)/(t)`

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:

`a=(57.21m/s)/(5*10^(-3)s)=11443.2(m)/(s^2)\\\\F=(5.85*10^(-3)kg)(11443.20m/s^2)=66.94N`

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