Question

A ball thrown from position A against a smooth circular wall rebounds and hits position B at the other end of the diameter through A. If the coefficient of restitution between wall and ball is $e$ and $\theta ={30}^{\circ }$, find $3e$. Do not consider any force on ball except contact force due to the wall at the time of the collision.

• A. $1$
• B. $\frac{1}{4}$
• C. $\frac{1}{5}$
• D. $\sqrt{3}$

Answer 1

Answer: (A)

$1$

$vsin\theta =eucos\theta$ .................... (1)
$vcos\theta =usin\theta$ ..................... (2)

Dividing (1) by (2), we get:
$tan\theta =\frac{e}{tan\theta }$
So, $e=ta{n}^2\theta =\frac{1}{3}$
Or, $3e=1$