A tennis player swings her 1000 g racket with a speed of 11 m/s. She hits a 60 g

Question

A tennis player swings her 1000 g racket with a speed of 11 m/s. She hits a 60 g tennis ball that was approaching her at a speed of 18 m/s. The ball rebounds at 36 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? How does this compare to the gravitational force on the ball? Favg / Wball =

Explanation / Answer

(a) Here, momentum before impact = 1.0 * 11 – 0.06 * 18 = 9.92 kgm/s

And momentum after the impact = 1.0 * V + 0.06 * 36 = V + 2.16

Apply conservation of momentum -
9.92 = V + 2.16

=> V = 7.76 m/s
So, Vracket = 7.76 m/s

(b) F . t = mv

F (average) = 0.06 ( 36 – – 18) / (6 * 10^–3) = 540 N

Now, Wball = mg = 0.06*9.81 = 0.5886 N

So, Favg / Wball = 540 / 0.5886 = 917.4

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