Question

A tennis ball hits the floor with a speed $v$ at an angle $\theta$ with the normal to the floor. If the collision is inelastic and the co-efficient of restitution is $\epsilon$, what will be the angle of reflection?

• A. ${\tan }^{-1}\left(\frac{\tan \theta }{\epsilon }\right)$
• B. ${\sin }^{-1}\left(\frac{\sin \theta }{\epsilon }\right)$
• C. $\theta \epsilon$
• D. $\theta \frac{2\epsilon }{\epsilon +1}$

Answer 1

Answer: (A)

$\tan {\theta }^{\prime }=\frac{u\sin \theta }{eu\cos \theta }$
$\tan {\theta }^{\prime }=\frac{1}{e}\tan \theta$
Since the floor is smooth. Hence tangential component of velocity remains unchanged