Question

The coefficient of restitution for a body is $e=\frac{1}{3}$ . At what angle the body must be incident on a perfectly hard plane so that the angle between the direction before and after the impact be at right angles?

• A. $37^\circ $
• B. $60^\circ $
• C. $45^\circ $
• D. $30^\circ $

Answer 1

Answer: (D)

$tan \phi=\frac{1}{e}tan ⁡ \theta $
Given $\theta +\phi=90^\circ $
$\therefore \, \, tan \left(90 ^\circ - \theta \right)=\frac{1}{\left(\frac{1}{3}\right)}tan ⁡ \theta $
$cot \theta \left(\frac{1}{3}\right)=tan ⁡ \theta $
$tan^{2} \theta =\frac{1}{3}$
$tan \theta =\frac{1}{\sqrt{3}}$
$\theta =30^\circ $