Question

A few years ago, Serena Williams dived to hit a tennis ball right after it bounced off the ground. The ball bounced on the ground 11.3 m from the net, and after Serena hit the ball it flew over the 0.950-m-high net and bounced in her opponent\'s court about 1.06 s after she hit it. If there had been no gravity, the ball would have been 1.82 m higher than the net when it crossed over. How fast was the ball moving when it left Serena\'s racket? Ignore any effects from ball spin and air resistance.

Answer 1

Let the speed of the ball of the racket = x m/s

Let the angle with the horizontal =

Horizontal speed = v cos

Vertical speed = v sin

Case 1. with gravity

time for ball to reach net = 1.06 / 2 = 0.53 m ( since it will be half the time to bounce off opponents court, assuming that the ball crosses the net when it is at its highest point )

horizontal distance = 11.3 m

Horizontal speed v cos = 11.3 / 0.53 = 21.32 m/s

v cos = 21.32 m/s (eq 1)

Case 2. without gravity

vertical distance = 0.95 + 1.82 = 2.77 m

initial vertical speed = v sin

a = 0

time will remain same = 0.53 second to reach net as there has been no change in acceleration or velocity in horizontal direction

=> 2.77 = 0.53 v sin

=> v Sin = 5.226 m/s (eq 2)

From eq 1 and eq 2, we get

= 13.77 degrees

v = 21.95 m/s

So the ball was moving at 21.95 m/s off the racket