Question

Consider the problem of returning a serve in tennis. A serve is hit at a speed of 67.7 m/s, and is hit back to the server with a speed of 40.8 m/s. The ball of mas m = 57 g is in contact with the racket for 0.01s.

(a) What is the magnitude of the impulse imparted to the ball as it is returned to the server?
(b) Estimate the magnitude of the average force on the ball.

Answer 1

Step-by-step explanation:

Given

mass of ball
`m=57 gm`

initial velocity
`v_1=67.7 m/s`

Final velocity
`v_2=40.8 m/s` (in opposite direction)

(a)Impulse imparted=Change in momentum

Impulse
`=\Delta P`

Impulse
`=m(v_1-v_2)`

Impulse
`=0.057(67.7-(40.8))`

Impulse
`=0.057* 108.5=6.184 kg-m/s`

(b)Magnitude of Average Force

`F_(avg)\cdot dt=\Delta P`

`F_(avg)=(6.184)/(0.01)=618.45 N`