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 19 m/s . The ball rebounds at 35 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?

Answer 1

here,

mass of racket , m1 = 1000 g

mass of tennis ball , m2 = 60 g

initial speed of racket , u1 = 11 m/s

initial speed of ball , u2 = - 19 m/s

final speed of ball , v2 = 35 m/s

a)

let the final speed of racket be v1

using conservation of momentum

m1 * u1 + m2 * u2 = m1 * v1 + m2 * v2

1000 * 11 - 60 * 19 = 1000 * v1 + 60 * 25

v1 = 8.36 m/s

b)

time taken , t = 10 ms = 0.01 s

the average force that the racket exerts on the ball , F = impulse /time

F = m1 * ( v1 - u1) /t

F = 1 * ( 11 - 8.36)/0.01 N

F = 264 N