Answer :

The initial velocity of both the gun and the shell system is zero

The initial momentum of the system = 0


Given,


Mass of the gun, M = 100 kg


Mass of the shell, m =0.02 kg


Final speed of the muzzle of the shell, v = 80 m/s


We suppose the recoil speed of the gun to be V.


The final momentum of the system = mv – MV


The negative sign is because the direction of motion of gun and shell is opposition to each other.



According to the law of conservation of linear momentum:


Total initial momentum = Total final momentum


Therefore,


0 = mv – MV



= 0.016 m/s


The recoil speed of the gun is 0.016 m/s


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