A sphere `A` is released from rest in th position shown and strikes the block `B` which is at rest. If `e=0.75` between `A` and `B` and `mu_(k)=0.5` between `B` and the support, determine
(a) the velocity of `A` just after the impact
(b) the maximum displacement of `B` after the impact.

Answer

`v_(A)=sqrt(g//12)m//s,S_("max")=49//48 m`

Explanation

velocity of block `A` just before collision `=sqrt(2gh)`
`=sqrt(2(g)(1.5))=sqrt(3g)

Conservation of momemtum
`2sqrt(3g)+4(0)=2v_(1)+4v_(2)`
`rArr " "v_(1)+2v_(2)=sqrt(3g)`
`e=0.75=(3)/(4)=(v_(2)-v_(1))/(sqrt(3g))" "rArrv_(2)-v_(1)=(3)/(4)sqrt(3g)`
`rArr" "v_(1)=-sqrt((g)/(12))" 'v_(2)=(7)/(4)sqrt((g)/(3))`
Maximum displacement of block `B=(v_(2)^(2))/(2mug)`
`=((49)/(16)((g)/(3)))/(2((1)/(2))g)=(49)/(48)m`