Final answer:
The velocity of recoil of the gun is 15 m/s to the left.
Step-by-step explanation:
The velocity of recoil of a gun can be determined using the principle of conservation of momentum. When a bullet is fired from a gun, the gun and the bullet experience equal and opposite momentum changes due to their interaction.
Given that the mass of the bullet is 15 grams (0.015 kg) and its velocity is 1000 m/s to the right, the momentum of the bullet can be calculated by multiplying its mass and velocity.
Momentum of the bullet = mass x velocity = 0.015 kg x 1000 m/s = 15 kg m/s to the right.
According to the principle of conservation of momentum, the momentum of the gun and the bullet before the firing is zero, so the momentum after the firing must also be zero. Since the bullet has a momentum of 15 kg m/s to the right, the gun must have an equal and opposite momentum to the left.
Therefore, the velocity of recoil of the gun is 15 m/s to the left.