A table-tennis player moves his bat up and down in such a way that the ball always bounces to a height of 0.45 m from the bat. Coefficient of restitution is 0.5. What is the speed (in m/s) of the bat when hitting the ball? (The mass of the ball is much less than that of the bat and air resistance is also negligible.)

Engineering

Physics

Collision

Question

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Velocity of ball just before striking the bat $v_{0} = \sqrt{2 gh}$

$e = \frac{v_{0} - v_{b}}{v_{0} + v_{b}} \Rightarrow y_{b} = \frac{v_{0} (1 - e)}{1 + e} = \sqrt{2 gh} \frac{(1 - e)}{1 + e} = 1$

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