We will first calculate the momentum of bullet and of the rifle separately and then apply the law of conservation of momentum.
(i) Momentum of bullet=Mass of bullet `xx` Velocity of bullet
`=50/1000kgxx35ms^(-1)`
`=0.05kgxx35ms^(-1)`
`=1.75 kg ms^(-1)`.....(1)
(ii) Suppose the recoil velocity of the rifle is v `ms^(-1)`. So,
Momentum of rifle=Mass of rifle`xx`Velocity of rifle
`=4kgxxvms^(-1)`
`=4vkgms^(-1)`
Now, according to the law of conservation of momentum:
Momentum of bullet=Momentum of rifle
So, 1.75=4v
And `v=1.75/4`
`v=0.4375ms^(-1)`
Thus, the recoil velocity of the rifle is 0.4375 metres per second.
