__Question 5.19__:
A
shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the
muzzle speed of the shell is 80 m
s

^{–1}, what is the recoil speed of the gun?

__Solution__:Mass of the gun,

*M*= 100 kg

*m*= 0.020 kg

Muzzle speed of the shell,

*v*= 80 m/s

Recoil speed of the gun =

*V*

Both the gun and the shell are at rest initially.

Initial momentum of the system = 0

Final momentum of the system =

*mv*–

*MV*

Here, the negative sign appears because the directions of the shell and the gun are opposite to each other.

According to the law of conservation of momentum:

Final momentum = Initial momentum

mv – MV = 0

∴ V = mv / M

= 0.020 X 80 / (100 X 1000) = 0.016 m/s

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