Question

A ball moving with a velocity $v$ hits a massive wall moving towards the ball with a velocity $u$ . An elastic impact lasts for a time $\Delta t$ .

• A. the average elastic force acting on the ball is $\frac{m \left(u + v\right)}{\Delta t}$
• B. the average elastic force acting on the ball is $\frac{2 m \left(u + v\right)}{\Delta t}$
• C. the kinetic energy of the ball increases by $mu\left(u + v\right)$
• D. the kinetic energy of the ball remains the same after the collision.

Answer 1

Answer: (B)

As the wall is massive its velocity remains unchanged.
Speed of the ball after impact $\bar{v}_{f}=v+2u$
The average elastic force acting on the ball is,
$\bar{F}=\frac{m \Delta \bar{v}}{\Delta t}=\frac{m \left[\bar{v}_{f} - \bar{v}_{i}\right]}{\Delta t}$
$F=\frac{m \left[\left(v + 2 u\right) - \left(- v\right)\right] \, }{\Delta t}=\frac{2 m \left(u + v\right)}{\Delta t}$
$F=\frac{2 m \left(u + v\right)}{\Delta t}$