A gun of mass 5k g fires a bullet of mass 20 g with a speed of 100 m/s. Find the recoil velocity of the gun

Mass of bullet, m=20g=  0.02kg

Velocity of bullet, v=100m/s  

Mass of gun, M=5kg

Let recoil velocity of gun =V

Before firing, the system (gun+bullet) is at rest, therefore, initial momentum of the system =0

Final momentum of the system = momentum of bullet + momentum of gun

=mv+MV=  

=2+5v

we know Final momentum = Initial momentum

i.e., 2+5v=0

5V=−2

v=-0.4m/s  

Negative sign shows that the direction of recoil velocity of the gun is opposite to the direction of the velocity of the bullet.

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