Question

A ball of mass $m$ hits the floor with a speed ${\nu }_0$ making an angle of incidence $\alpha$ with the normal. The coefficient of restitution is i.e. Find the speed of the reflected ball and the angle reflection of the ball.

Answer 1

the component of velocity ${\nu }_0$ along common tangent direction ${\nu }_{0}sin\alpha$ remain unchanged. Let $\nu$ be the component along common normal direction after collision. Applying relative speed of separation $=e\times$ (relative speed of approach) along common normal direction, we get
$\nu =e{\nu }_{0}cos\alpha$
Thus, after collision components of velocity ${\nu }^{\prime }$ are ${\nu }_{0}sin\alpha$ and $e{\nu }_{0}cos\alpha$.
$\therefore {\nu }^{\prime }=\sqrt{({\nu }_{0}sin\alpha {)}^2+(e{\nu }_{0}cos\alpha {)}^2}$
and $tan\beta =\frac{{\nu }_{0}sin\alpha }{e{\nu }_{0}cos\alpha }=\frac{tan\alpha }{e}$