A particle of mass `m` is moving horizontally with a constant velocity `v` towards a rigid wall that is moving in opposite direction with a constant speed `u`. Assuming elastic impact between the particle and wall, the work done by the wall in reflecting the particle is equal to

Options

A. `(1//2)m(u+v)^(2)`
B. `(1//2)m(u+v)`
C. `(1//2)muv`
D. `2mu(u+v)`

Explanation

Velocity of separation `=-e` (velocity of approach)
`rArr(-v'i)-(ui)=-e[(v_(i))-(-u_(i))]`
`rArru-v'=-1(v+u)`
`rArrv'=2u+v`
`:. W=DeltaK.E.=(1)/(2)mv'^(2)-(1)/(2)mv^(2)`
`=(1)/(2)m[(2u+v)^(2)-v^(2)]=2mu(u+v)`