Question

Short answer

The speed of a tennis ball can be as fast as the serve on the return even if the racket is not swung very fast because of the momentum imparted by the racket on the ball during its return.

Step-by-step solution

Momentum conservation of the ball

The conservation of momentum principle states that the total momentum of an isolated system remains conserved. In this case, the served tennis ball returning from the little swung racket will take the momentum of the racket as the mass of the racket is more than the ball, and it will add to the velocity of the tennis ball.

Determine the energy and velocity of the rebounded tennis ball

When the tennis ball is served toward the other end, where the ball hits straight onto the slowly swung racket, it rebounds with the reverse velocity components. The small kinetic energy lost during the collision with the racket is compensated by the velocity imparted to the tennis ball by the racket. From the momentum conservation principle, a slowly moving racket with a larger mass than the ball will impart higher velocity to it. Therefore, the ball on return can be as fast as the serve.