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 time of flight of the shell is:

Options

A. `(u cos theta)/(g sin beta)`
B. `(2u sin theta)/(g cos beta)`
C. `u/g`
D. `(u sin theta)/(g sin beta)`

Answer

B

Explanation

`a_(x)=-g sin beta , U_(x)=U cos theta`
`a_(y)=-g cos beta , V_(x)=V sin theta`
Time of flight `T=(2V_(y))/a_(y)=(2Vsin theta)/(g cos beta)`