From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 m s⁻¹. Calculate the initial recoil velocity of the rifle.

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

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