A tennis player receives a shot with the ball (0.0600 kg) traveling horizontally

Question

A tennis player receives a shot with the ball (0.0600 kg) traveling horizontally at 17.0 m/s and returns the shot with the ball traveling horizontally at 39.0 m/s in the opposite direction. (Assume the initial direction of the ball is in the -x direction.) (a) What is the impulse delivered to the ball by the tennis racket? I N s (b) Some work is done on the system of the ball and some energy appears in teh ball as an increase in internal energy during the collision between the ball and the racket. What is the sum W - DeltaE_int for the ball? J

Explanation / Answer

We assume that the initial direction of the ball is in the –x direction.
(a) The impulse delivered to the ball is given by
I = p = pf pi
= (0.060 0 kg)(39.0 m/s)ˆi (0.060 0 m/s)(17.0 m/s)(ˆi)
= 1.32ˆi N*s

We choose the tennis ball as a nonisolated system for energy. Let the time interval be from just before the ball is hit until just after.

K+Eint =Tmw

Solving for the energy sum Eint Tmw and substituting gives
E T =K
(1/2mvf^2 1/2mvi^2) = 1/2m(vi^2 vf^2)

-1/2(0.06kg)[17^2 - 39.^2] = 36.96J

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