The rebound coefficient between a tennis ball | vedclass

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Question

(A) The coefficient of restitution $e$ is given by the ratio of speeds when the racket is at rest: $e = \sqrt{h/H} = \sqrt{0.8 H / H} = \sqrt{0.8} \ap

Vedclass · Accepted Answer

$323.6$

Vedclass · Answer

(A) The coefficient of restitution $e$ is given by the ratio of speeds when the racket is at rest: $e = \sqrt{h/H} = \sqrt{0.8 H / H} = \sqrt{0.8} \approx 0.8944$.Let the ball move in the positive direction with velocity $v_b = 150 \ km/hr$ and the racket move in the negative direction with velocity $v_r = -100 \ km/hr$.The relative velocity of the ball with respect to the racket is $v_{rel} = v_b - v_r = 150 - (-100) = 250 \ km/hr$.After the collision,the relative velocity of the ball with respect to the racket $v'_{rel}$ is given by $v'_{rel} = -e \cdot v_{rel} = -0.8944 	imes 250 \approx -223.6 \ km/hr$.Since the mass of the racket is much greater than the mass of the ball,the velocity of the racket remains unchanged at $v_r = -100 \ km/hr$.The final velocity of the ball $v'_b$ is $v'_b = v'_{rel} + v_r = -223.6 + (-100) = -323.6 \ km/hr$.The speed of the ball is the magnitude of the velocity,which is $323.6 \ km/hr$.

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