A cannon is fixed with a smooth massive trolley car at an angle `theta` as shown in the figure.The trolley car slides from rest down the inclined plane of angle of inclination `beta`.
The muzzle velocity of the shell fired at `t=y_(0)` from the cannon is `u`,such that the shell moves perpendicular to the inclined just after the firing.
The value of `t_(0)` is:

Options

A. `(u cos theta)/g`
B. `(u cos theta)/(g cos theta)`
C. `(u cos theta)/(g sin beta)`
D. `(u sin theta)/(g cos theta)`

Answer

C

Explanation

Velocity along tralley is zero i.e., `V_(x)=U_(x)+a_(x)t`
`0=U cos theta-(g sin beta)t, t=(U cos theta)/(g sin beta)`