Two blocks `A` and `B` of mass `m` and `2m` respectively are moving towards a massive (`"mass" gt gt 2m`) cliff with velocities `2v` and `v` respectively. The cliff moves with a velocity `v`. If the coefficient of restitution of collision at the surface of the cliff is `e = 1//2`, find the:

a. velocity of the block `B` just after colliding with the cliff.
b. work done by the cliff during collision.
c. maximum compression of the spring of stiffness `k` which is fitted with the block `B`.

Answer

`v/2`, `mv^(2), `v`

Explanation

As the cliff is very heafy so its velocity almost remains same after collision.
Let velocilty of block `B` just after Collision be `v_(1)`
`v_(2)-v_(1)=e[u_(1)u_(2)]`
`impliesv-v_(1)=1/2[2-v]impliesv_(1)=v/2` b. work done by clif =change in `KE` of `m`
`1/2m[(v/2)^(2)-(2)^(2)]a=-15/8mv^(2)`
c. Just after collision with cliff

At maximum compression
`COLM: 2mv_(0)+mv_(0)=2mv+(mv)/2impliesv_(0)=5/6v`
COME:` 1/2kx_(m)^(2)+1/2(3m)v_(0)^(2)=1/2(2m)v^(2)+1/2m(v/2)^(2)`
`implies x_(m)=(sqrt(m/(6k)))v`