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)"mu"v`
D. none of these

Answer

D

Explanation

`e=(v_(2)-v_(1))/(u_(1)-u_(2))implies1=(-u-(-v'))/(v-(-u))`

`impliesv'=2u+v`
`:. W=/_\KE=1/2mv^('2)1/2mv^(2)`
`=1/2m[(2u+v)^(2)]2"mu"(u+v)`