Hailstorms are observed to strike the surface of a frozen lake at an angle of `30^(@)` with the vertical and rebound at an angle of `60^(@)` with vertical. Assuming the contact to be smooth, the coefficient of restitution is

Options

A. `e=(1)/(sqrt(3))`
B. `e=(1)/(3)`
C. `e=sqrt(3)`
D. e=3

Answer

B

Explanation

Components of velocity befor and after collision parallel to the plane are equal ,So
v sin `60^(@)=usin30^(@)`
Componenets of velocity normal to the plane are related to each other
`v cos 60^(@)=e u(cos 30^(@))`
`impliescot60^(@)=ecot 30^(@)impliese=(cot 60^(@))/(cot 30^(@))`
`=e=(1)/(sqrt(3)/sqrt(3))impliese=(1)/(3)`.