Question

A steel ball strikes a fixed smooth steel plate placed on a horizontal surface at an angle $\theta$ with the vertical. If the coefficient of restitution is $e$, the angle at which the rebound will take place is

• A. $\theta$
• B. ${\tan }^{-1}\left[\frac{\tan \theta }{e}\right]$
• C. $e\tan \theta$
• D. ${\tan }^{-1}\left[\frac{e}{\tan \theta }\right]$

Answer 1

The correct option is B ${\tan }^{-1}\left[\frac{\tan \theta }{e}\right]$

$\text{Before collision}$

$\therefore u_x=u\sin \theta ,u_y=-u\cos \theta$

$\text{After collision}$

$\therefore v_x=u_x=u\sin \theta ,v_y=eu\cos \theta$

$\therefore tan\alpha =\frac{v_x}{v_y}=\frac{u\sin \theta }{eu\cos \theta }=\frac{\tan \theta }{e}$

$\therefore \alpha ={\tan }^{-1}\left(\frac{\tan \theta }{e}\right)$