Momentum troubles. Help?

Question

A tennis player swings her 1000 g racket with a speed of 9 m/s. She hits a 60 g tennis ball that was approaching her at a speed of 21 m/s. The ball rebounds at 37 m/s.

(a) How fast is her racket moving immediately after the impact? You can ignore the interaction of the racket with her hand for the brief duration of the collision.

(b) If the tennis ball and racket are in contact for 10 ms, what is the average force that the racket exerts on the ball?

(c) How does this compare to the ball's weight?

Answer 1

a) The ball's momentum is changed  by (21+37)m/s x 0.06kg

P = 3.48

Racket's momentum must be changed by that amount.

Initial momentum

P = 1kg x 9m/s = 9

final momentum = 9-3.48 = 5.52

final speed

5.52 = 1kg x V

V = 5.52 m/s

b) Ball must be accelerated enough that it's change in velocity is 58 m/s

this occurs in 10ms, so average acceleration is 58 m/s/.01s = 5800 m/s²

Use F = ma

F = 0.06 x 5800 m/s² = 348 Newtons.

c) balls weight is 0.06 kg x 9.8 = 0.59 Newtons

Compare? how?

ratio is 348/0.59 = 592

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