Mass of the rifle (m1) = 4 kg
Mass of the bullet (m2) = 50 g = 0.05 kg
Recoil velocity of the rifle = v1
A bullet is fired with an initial velocity (v2) = 35 m/s
Solution
Initially, the rifle is at rest.
Thus, its initial velocity (v) = 0
The total initial momentum of the rifle and bullet system
⇒ (m1+m2) × v = 0
The total momentum of the rifle and bullet system after firing
= m1v1 + m2v2
= (4 × v1 ) + (0.05 × 35)
= 4v1 + 1.75
According to the law of conservation of momentum
Total momentum after the firing = Total momentum before the firing
4v1 + 1.75 = 0
v1= -1.75 / 4
v1 = – 0.4375 m/s
The negative sign indicates that the rifle recoils backwards with a velocity of 0.4375 m/s.