Understanding the Principle
This problem uses the principle of conservation of momentum. In a closed system (like the gun and bullet), the total momentum before firing is equal to the total momentum after firing.
* Momentum: A measure of an object's mass in motion. It's calculated as mass (m) times velocity (v): momentum (p) = m * v
Calculations
1. Initial Momentum: Before firing, the total momentum is zero because both the gun and the bullet are at rest.
2. Final Momentum: After firing, the bullet has momentum (m_bullet * v_bullet) in one direction, and the gun has momentum (m_gun * v_gun) in the opposite direction.
3. Conservation of Momentum Equation:
0 (initial momentum) = (m_bullet * v_bullet) + (m_gun * v_gun)
4. Solving for Recoil Velocity (v_gun):
* Rearrange the equation: v_gun = - (m_bullet * v_bullet) / m_gun
* Plug in the values: v_gun = - (0.0050 kg * 250 m/s) / 9 kg
* Calculate: v_gun ≈ -0.139 m/s
Result
The recoil velocity of the gun is approximately -0.139 m/s. The negative sign indicates that the gun recoils in the opposite direction of the bullet's motion.
