I guess by ’how hard’ you’re asking what the racquet speed has to be when it hits the ball. I can give a minimum estimate. Let’s say that the racquet has a lot more mass than the ball and that the collision loses no energy to sound and heat etc. the first approximation is pretty good, the second not so good. Both let us underestimate the speed needed.
Looking at the collision in the frame of reference where the ball is moving and the racquet standing still makes calculations easy. The way the collsion can conserve energy in that frame is for the ball to simply switch directions from moving toward the racquet to moving away. So the change in velocity of the ball is twice its velocity relative to the racquet.
In the frame of the tennis court, where the ball is initially at rest, the racquet must then initially be moving at least 73 mph. I wouldn’t be surprised if the real number were more like 100 mph, given our approximations.
Mike W.
Only the part of the racquet hitting the ball needs to move that fast. The handle can be moving a lot more slowly if the racquet is rotating while moving towards the ball, which is usually the case.
Tom
(published on 10/22/2007)
