Mass of the rifle, `m_(1) = 4 kg`
Mass of the bullet, `m_(2) = 50g = 0.05 kg `
Recoil velocity of the rifle `= v_(1)`
Bullet is fired with an initial velocity, `v_(2) = `35 m/s
Initially, the rifle is at rest.
Thus, its initial velocity, v = 0
Total initial momentum of the rifle and bullet system `= (m_(1) + m_(2))v = 0 `
Total momentum of the rifle and bullet system after firing:
`= m_(1)v_(1) + m_(2)v_(2) = 4(v_(1)) + 0.05xx35 = 4v_(1) + 1.75 `
According to the law of conservation of momentum:
Total momentum after the firing = Total momentum before the firing `4v_(1) + 1.75 = 0 `
` v_(1) = – 1.75//4 = – 0.4375 m//s`
The negative sign indicates that the rifle recoils backwards with a velocity of 0.4375 m/s
