Understanding the Concept

This problem applies the principle of conservation of momentum. In a closed system, the total momentum before an event (like firing a bullet) equals the total momentum after the event.

Calculations

1. Momentum of the Bullet:

* Momentum (p) = mass (m) * velocity (v)

* p_bullet = 0.060 kg * 575 m/s = 34.5 kg*m/s

2. Momentum of the Gun:

* Since the total momentum before firing is zero (gun and bullet are at rest), the momentum of the gun after firing must be equal and opposite to the bullet's momentum.

* p_gun = -34.5 kg*m/s

3. Recoil Velocity of the Gun:

* v_gun = p_gun / m_gun

* v_gun = -34.5 kg*m/s / 4.50 kg = -7.67 m/s

Answer

The recoil velocity of the gun is -7.67 m/s. The negative sign indicates that the gun moves in the opposite direction to the bullet.