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.
after what time should the shell be fired such that it will go vertically up?

Options

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

Answer

D

Explanation

`V_(x)=U_(x),((a_(x))cos beta)t= U cos (theta+beta)`
`g sin beta cos betat=U cos (theta+beta),t=(U cos (theta+beta))/(g sin beta cos beta)`