I've been presented to the following problem:(adsbygoogle = window.adsbygoogle || []).push({});

A tennis ball can achieve a speed of 100 km/h. During the contact between tennis racket and ball the ball's dimension in the direction of movement is halved. Estimate how long ball and racket are in contact with each other. It can be presumed that the force between ball and racket is constant during the collision.

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It isn't wholly clear, if we are to involve the deformation in our calculations, since the sentence "During the contact between tennis racket and ball the ball's dimension in the direction of movement is halved." might be just a statement about normal racket-ball collisions. Then we'd just have to estimate a force for a normal collision - a quite loose estimate, if we just guess. Or it might mean that we'd have to include the deformation x = r/2 - where r is the ball radius.

But how? We can't use work, since we'd just get W = Fs <=> F = W / (r/2) - if we assert that only the ball is elastic, which isn't true, and then we'd have to estimate the work instead of the force (since work doesn't come into the other relevant equations).

Using elastic potential energy U[el], we'd have to estimate a spring constant, which is even more loose than estimating force.

Is there an easy/right/good way? Or somewhere, at least, that I can find values of racket force or ball speeds immediately following collisions?

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# Tennis ball-racket collision: Deformation and duration

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