Question

From a rifle of mass 4 kg, a bullet of mass 50 g is fired horizontally with an initial velocity of 40 m/s. calculate the initial recoil velocity of the rifle

Answer 1

Given: Mass of rifle = 4 kg

Mass of bullet = 50 g = 0.05 kg

Initial velocity of the bullet = 35 m/s

Let the recoil velocity of the rifle be = v m/s

Since in the beginning both the rifle and bullet are at the rest (when bullet is not fired)

Therefore, initial momentum = 0

When the bullet is fired both bullet and rifle moves.

Therefore, final momentum = momentum of bullet + momentum of rifle

so,

Final momentum = (0.05 × 35)  + (4 x v)

= 1.75 + 4v

by applying law of conservation of momentum we get

1.75 + 4v = 0

or

4v = -1.75

thus, recoil velocity of the rifle will be

v = -0.4375 m/s