A steel ball strikes a fixed smooth steel plate placed on a horizontal surface at an angle `theta` with the vertical. If the coefficient of restitution is e, the angle at which the rebound will take place is:

Options

A. `theta`
B. `tan^(-1)[(tan theta)/(e)]`
C. `e tan theta`
D. `tan^(-1)[(e)/(tan theta)]`

Answer

B

Explanation

Before collision

`therefore u_(x)=u sin theta , u_(y)=-u cos theta`
After collision
`therefore v_(x)=u_(x)=u sin theta, v_(y)=eu cos tehta`
`therefore tan alpha=(v_(x))/(v_(y))=(u sin theta)/(eu cos theta)=(tan theta)/(e)`
`therefore alpha=tan^(-1)((tan theta)/(e))~