A railway flat car has an artillery gun installed on it. The combined system has a mass `M` and moves with a velocity `V`. The barrel of the gun makes an angle a with the horizontal. A shell of mass `m` leaves the barrel at a speed `v` relative to the barrel. The speed of the flat car so that it may stop after the firing is

Options

A. `(mv)/(M+m)`
B. `((Mv)/(M+m))cosalpha`
C. `(mv)/(M+m))cosalpha`
D. `(M+m))cosalpha`

Answer

C

Explanation

As the car stops so velocity of bullet after firing is same w.r.t ground and w.r.t car. Conservng momentum in horizontal direction.
`(M+m)v=mvcosalphaimpliesV=(mvcosalpha)/(M+M)`