Question

A 10 g bullet is shot from a 5 kg gun with a velocity of 500 m/s . What is the recoil velocity of the gun?​

Answer 1

• Mass of the bullet, m = 10 g

$1 \: g \: = {10}^{ - 3} \: kg \\ \\ 10 \: g \: = 10 \times {10}^{ - 3 \: kg } \\ \\ m \: = {10}^{ - 2} \: kg$

• Velocity of the bullet, v = 500 m/s.

• Mass of the gun, M = 5 kg

• Let the recoil velocity of gun be V.

Momentum is equal to the product of mass and velocity.

Momentum ,p = mv

According to law of conservation of momentum, Initial total momentum = Final total momentum

mv + MV = 0

$m \times v \: = -M \times V \\ \\ {10}^{ - 2} \times 500 = -5 \times V \\ \\ {10}^{ - 2} \times 5 \times {10}^{2} = -5 \times V \\ \\ 5 = -5 \times V \\ \\ V = \frac{5}{-5} \\ \\ V = -1 \: \frac{m}{s}$

The recoil velocity of the gun is 1 m/s.