Question

A ball reaches a racket at $60m/s$ along +x direction, and leaves the racket in the opposite direction with the same speed. Assume that the mass of the ball is $50gm$ and the contact time is $0.02$ second. With the force exerted by the racket on the ball, which of the following can be done? (Take $g=10m/s^2$)

• A. We can lift a load 300kg off the ground.
• B. We can lift a 30 kg child off the ground.
• C. We can lift a 90 kg stone off the ground.
• D. We can lift a 300 tonnes truck off the ground.

Answer 1

Answer: (B)

We can lift a 30 kg child off the ground.

Initial momentum, $p_i=0.05\times 60=3kgm/s$
Final momentum, $p_f=0.05\times -60=-3kgm/s$
$\therefore$ Change in momentum $△P=-6kgm/s$
$\overrightarrow{F}=\frac{△\overrightarrow{P}}{△t}=\frac{-6}{0.02}=-300N$
$\therefore$ A force of magnitude $300N$ is generated and we can lift a $30kg$ child off the ground by this force.