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# Hail storms are observed to strike the surface of frozen lake at $30^{\circ }$ with the vertical and rebound at $60^{\circ}$ with vertical, Assume contact to be smooth, the coefficient of restitution,

$(a)\;e=\frac{1}{\sqrt 3} \quad (b)\;e=\frac{1}{3} \quad (c)\;e=\sqrt 3 \quad (d)\;e=3$

Comparing velocities before and after collision parallel to the plane surface
$v \sin 60^{\circ}=u \sin 30^{\circ}$
Comparing components of velocity normal to the surface
$v \cos 60=eu \cos 30^{\circ}$
$\cot 60=e \cot 30^{\circ}$
$e=\large\frac{\cot 60}{\cot 30}$
$e= \large\frac{\Large\frac{1}{\sqrt 3}}{\sqrt 3}$
$e=\large\frac{1}{3}$
Hence b is the correct answer

edited Feb 10, 2014 by meena.p