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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 time Δt.

A
The average elastic force acting on the ball is [m(u+v)]Δt.
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B
The average elastic force acting on the ball is [2m(u+v)]Δt. ​​​​
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C
The kinetic energy of the ball increases by 2mu (u + v)
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D
The kinetic energy of the ball remains the same after the collision.
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Solution

The correct option is C The kinetic energy of the ball increases by 2mu (u + v)
In an elastic collision : vsep=vapp
or vu=v+u or v=v+2u

Chnage in momentum of ball is
|PfPi|=|m(v)mv|=m(v+v)=2mu(u+v)
Average force is ΔPΔt=2m(u+v)Δt
Change in KE,KfKi=12mv212mv2=2m u (u + v)

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