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.
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)
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