Question

In tennis, the speed of the ball can reach 60 m/s in a fast service. How fast must the tennis racket be swung to reach that speed? Assume the mass of the racket is much larger than the mass of the ball.

Answer 1

Assume it is an enastic collision. Let mass of raquet be m1 and mass of ball m2.And initial and final vlocities be u1,v1 and u2,v2 . Given m1>>m2. v2=60, u2=0(typically) we need to find u1.

Now in an elastic collision, final velocity can be given by v2= (m2-m1)/(m1+m2) *u2 + 2m1/(m1+m2) *u1. substitutimg known values, we get: 60=0+ 2m1/(m1+m2) *u1 now since m1>>m2, m1+m2~m1. That gives us 60=2u1

Therefore the velocity of raquet should be half the required velocity, which in this case should be 30m/s