A bullet of mass $50\ g$ is fired from a gun of mass $6\ kg$ with a velocity of $400\ m/s$. Calculate the recoil velocity of the gun.

Given: Mass of the bullet $m_{bullet}=50\ g=\frac{50}{1000}\ kg=0.05\ kg$

Mass of the gun $m_{gun}=6\ kg$

Final velocity of the bullet $=400\ m/s$

To do: To find the recoil velocity of the gun.

Solution:

Let $v$ be the recoil velocity of the gun.

According to the law of conservation of momentum:

Total momentum of Bullet and gun before firing$=$Total momentum of the bullet and gun after firing

Or $0.05\times 0+6\times0=0.05\times400+6\times v$

Or $0=20+6v$

Or $v=-\frac{20}{6}$

Or $v=-3.33\ m/s$    [-ve sign indicates the opposite direction]

Therefore, the recoil velocity of the gun is $3.33\ m/s$ in the opposite direction.

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Updated on: 10-Oct-2022

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