Question

A 58.0 g incoming tennis ball has a speed of 30 m/s when it is hit by a

racket in the opposite direction and leaves the racket at 40 m/s. What
is the average force exerted by the racket on the ball if contact lasted
for 5.2 ms?

Answer 1

The racket applies an average acceleration of

`a_(\rm ave) = (\Delta v)/(\Delta t) \\\\ a_(\rm ave) = (40(\rm m)/(\rm s) - \left(-30(\rm m)/(\rm s)\right))/(5.2\,\rm ms) = (40(\rm m)/(\rm s) - \left(-30(\rm m)/(\rm s)\right))/(0.0052\,\rm s) = 13,461.5(\rm m)/(\mathrm s^2)`

(Note that I'm taking the initial direction of the ball's motion to be negative.)

Then the average force exerted on the ball is

`F_(\rm ave) = ma_(\rm ave) \\\\ F_(\rm ave) = (58.0\,\mathrm g)a_(\rm ave) = (0.058\,\mathrm{kg})a_(\rm ave) \approx \boxed{780\,\mathrm N}`