Question

A gun is mounted on a stationary rail road car. The mass of the car, the gun, the shells and the operator is 50m, where m is the mass of one shell. Two shells are fired one after the other along same horizontal line in same direction. If the muzzle velocity (velocity with respect to gun) of the shells is 200 m/s, then find the speed of the car after second shot.

Answer 1

Centre of mass of velocity of shell $=0$ (initially at rest)

Therefore , $0=49m\times V+m\times 200$

$V=\frac{-200}{49}m/s$

$\frac{200}{49}m/s$ towards left .

Another shell is fire , then the velocity of the car , with respect to platform is

$V^{\prime }=\frac{200}{49}m/s$ towards left.

Another shell is fired , then the velocity of the car with respect to platform is

$v^{\prime }=\frac{200}{48}m/s$ towards left.

Now , the velocity of the car with respect to earth is $(\frac{200}{49}+\frac{200}{48})=\frac{19400}{2352}=8.24m/s$ towards left.