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 $\frac{2m\left(u+v\right)}{\Delta t}$
• 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,
$\bar{F}=\frac{m\Delta \bar{v}}{\Delta t}=\frac{m\left[{\bar{v}}_f-{\bar{v}}_i\right]}{\Delta t}$
$F=\frac{m\left[\left(v+2u\right)-\left(-v\right)\right]}{\Delta t}=\frac{2m\left(u+v\right)}{\Delta t}$
$F=\frac{2m\left(u+v\right)}{\Delta t}$