The mass of the bullet, m1 = 15 g = 0.015 kg
Mass of the pistol, m2 = 2 kg
Initial velocity of the bullet, u1 = 0
Initial velocity of the pistol, u2 = 0
Final velocity of the bullet, v1 = + 100 ms-1
(The direction of the bullet is taken from left to rightpositive, by convention)
Recoil velocity of the pistol = v2
Total momentum of the pistol and bullet before firing.
= m1 u1 + m2 u1
= (0.015 × 0) + (2 × 0)
Total momentum of the pistol and bullet after firing.
= m1v1 + m2v2
= (0.015 × 100) + (2 × v2)
= 1.5 + 2v2
According to the law of conservation of momentum, Total momentum after firing = Total momentum before firing.
1.5 + 2v2 = 0
2v2 = -1.5
v2 = – 0.75 ms-1
Negative sign indicates that the direction in which the pistol would recoil is opposite to that of the bullet, that is, right to left.