Question

A railway flat car, the mass of which together with the artillery gun is $M$, moves at a speed $V$. The gun barrel makes an angle $a$ with horizontal. A shell of mass $m$ leaves the barrel at a speed $v$, relative to the barrel. The speed of the flat car in order that it may stop after the firing is :

• A. $\frac{mv\cos a}{M+m}$
• B. $\frac{mv}{M+m}$
• C. $(M+m)v\cos a$
• D. $\frac{Mv\cos a}{M+m}$

Answer 1

The correct option is A $\frac{mv\cos a}{M+m}$

To stop the cart, initial horizontal momentum of $cart+barrel$ system should be same as final momentum of barrel w.r.t the cart .i.e.,

$(M+m)V=mv\cos \left(a\right)$

$V=\frac{mvcosa}{M+m}$