Solve the following :
Question:

A gun is mounted on a railroad car. The mass of the car, the gun, the shells and the operator is $50 \mathrm{~m}$ where $\mathrm{m}$ is the mass of one shell. If the velocity of the shell with respect to the gun (in its state before firing) is $200 \mathrm{~m} / \mathrm{s}$, what is the recoil speed of the car after the second shot? Neglect the friction.

Solution:

After 1 bullet,

C.O.L.M $\Rightarrow 0=49 m \times V_{1}+m(200)$

$\Rightarrow V_{1}=\frac{-200}{49}$

After $2^{\text {nd }}$ bullet C.O.L.M $\Rightarrow 0=48 m \times V_{2}+(200) m$

$\Rightarrow V_{2}=\frac{-200}{48}$

$V_{\text {car }}=V_{1}+V_{2}=-200\left(\frac{1}{49}+\frac{1}{48}\right)_{\mathrm{m} / \mathrm{s}}$

(after $2^{\text {nd }}$ shot)