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

Answer:

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

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

The total momentum of the rifle and bullet system after firing

= m1v1 + m2v2

= (4 × v) + (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

v= – 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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