To find the velocity of the recoil of the gun, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the bullet is fired is equal to the total momentum after the bullet is fired.
Let's denote the mass of the bullet as m₁ = 150 g = 0.15 kg and the mass of the gun as m₂ = 15 kg. The initial velocity of the bullet is v₁ = 1000 m/s, and we need to find the recoil velocity of the gun, which we'll denote as v₂.
Using the conservation of momentum, we can write:
m₁ * v₁ + m₂ * 0 = 0 + (m₁ + m₂) * v₂
Here, the left side of the equation represents the initial momentum before the bullet is fired, and the right side represents the final momentum after the bullet is fired.
Simplifying the equation:
0.15 kg * 1000 m/s = (0.15 kg + 15 kg) * v₂
150 kg·m/s = 15.15 kg * v₂
Dividing both sides of the equation by 15.15 kg:
v₂ = 150 kg·m/s / 15.15 kg
v₂ ≈ 9.90 m/s
Therefore, the velocity of the recoil of the gun is approximately 9.90 m/s.