Question

A small ball of mass $m$ collides with a rough wall having coefficient of friction $\mu$ at an angle $\theta$ with the normal to the wall. If after collision the ball moves angle $\alpha$ with the normal to the wall and the coefficient of restitution is $e$, then find the reflected velocity $\nu$ of the ball just after collision.

Answer 1

The velocity component along the wall does not change.

Hence, $v\sin \alpha =u\sin \theta$

And for component of velocity normal to wall-

$e=\frac{v\cos \alpha }{u\cos \theta }$

$⟹v\cos \alpha =eu\cos \theta$

Hence, $\tan \alpha =\frac{\tan \theta }{e}$

And, $v=u\sqrt{{\sin }^2\theta +e^2{\cos }^2\theta }$