A bullet of mass 20g is fired horizontally with a velocity of 150 m/s from a pistol of mass 2 kg. Find the recoil velocity of the pistol.

Given Mass of bullet, m1 = 20 g = 0.02 kg

Mass of pistol, m2 = 2 kg

Initial velocity of the bullet (u1) and pistol, u2 = 0

Final velocity of the bullet, v1 = 150 ms-1

Let the recoil velocity of the pistol be v

The total momentum of the pistol and bullet is zero before the fire (because both are at rest)

The total momentum of the pistol and bullet after it is fired is

= (0.02 kg x 150 ms-1) + (2 kg x v ms-1)

On calculation, we get,

= (3 + 2v) kg ms-1

Total momentum after the fire = Total momentum before the fire

3 + 2v = 0

2v = -3

v = -3/2

v = -1.5 m/s

Hence, the recoil velocity of the pistol is 1.5 m/s

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