A ball rolls without sliding over a rough horizontal floor with velocity `v_(0)=7m//s` towards a smooth vertical wall. If coefficient of restitution between the wall and the ball is `e=0.7`. Calculate velocity `v` of the ball long after the collision.

Explanation

between A and B, there is forwards slippoing therefore, friction will be maximum and backwards (rightwards) at point B where `v=Romega`, ball starts rolling without slippoing and force of friction becomes zero.
form conservation of angular momentum between point A and B about bottommost point (because torque of friction about this point is zero)
`thereforem(0.7v_(0))R-Iomega_(0)=mvR+Iomega`
substituting `omega_(0)=(v_(0))/(R),omega=(V)/(R)`
and `I=(2)/(5)mR^(2)` we get
`v=(3)/(14)v_(0)=((3)/(14)(7)m//s=1.5m//s`