A ball moving with a velocity `v` hits a massive wall moving towards the ball with a velocity a. An elastic impact lasts for time `/_\t`

Options

A. The average elastic force acting on the ball is `[m(u+v)]///_\t`
B. The average elastic force acting on the ball is `[2m(u+v)\]///_\t`
C. The kinetic energy of the ball increases by `2"mu" (u + v)`.
D. The kinetic energy of the ball remains the same after the collision.

Answer

B, C

Explanation

In an elstic collision `v_(sep)=v_(app)`
or `v'-u=v+u` or `v'=v+2u`

change in momentum of ball is
`|p_f-p_i|=|m(-v')-mv|=m(v'+v)=2mu(u+v)`
Average force is `(/_\P)/(/_\t)=(2m(u+v))/(/_\t)`
change in `KE`, `K_(f)-K_(i)=1/2mv^('2)=2mu(u+v)`