Question

A wedge of mass $M$ is kept at rest on smooth surface, a particle of mass $m$ hits the wedge normally. Find the velocity of wedge and particle just after collision. Take coefficient of restitution as $e$.

Answer 1

The impulse acting on the ball and wedge can be represented as
$Jsin\theta =MV$ (i)
$m\nu -J=m{\nu }_n$ (ii)
and Newton's law of restitutiion
$(\nu sintheta-{\nu }_n)=e({\nu }_0-0)$ (iii)
Solving Eqs. (i), (ii) and (iii), we get
$V=\frac{(1+e)m{\nu }_{0}sin\theta }{M+msi{n}^2\theta }$