Question

A steel ball strikes a steel plate 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 ${\tan }^{-1}\left[\frac{\tan \theta }{e}\right]$

Velocity of ball along the plate $\left(v\sin \theta \right)$ remains same after collision.
Velocity of the plane perpendicular to plate after collision is $\left(ev\cos \theta \right)$


$\tan \alpha =\frac{v\sin \theta }{ev\cos \theta }=\frac{\tan \theta }{e}$

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