An armature shooter holds a 4.50 kg rifle loosely ,allowing it to recoil freely when fired,and fires a bullet of mass 4.20 g horizontally with a speed of 900 ms^-1.What is the recoil speed of the rifle?

Explanation:

Another Explanation (5): let's break down how to calculate the recoil speed of the rifle 🔫 using the principle of conservation of momentum. 💪 **Understanding the Principle** The law of conservation of momentum states that the total momentum of an isolated system remains constant. In simpler terms, in a closed system (no external forces), the total momentum before an event (firing the rifle) equals the total momentum after the event. 🤓 **Applying it to the Rifle Scenario** 1. **Initial Momentum:** Before the rifle is fired, both the rifle and the bullet are at rest. Therefore, the total initial momentum of the system is zero. 😴 \(latex p_{initial} = 0\) 2. **Final Momentum:** After the rifle is fired, the bullet has momentum in one direction, and the rifle recoils with momentum in the opposite direction. Let: * \(latex m_r\) = mass of the rifle = 4.50 kg * \(latex v_r\) = recoil velocity of the rifle (what we want to find) * \(latex m_b\) = mass of the bullet = 4.20 g = 0.0042 kg (we need to convert to kg) * \(latex v_b\) = velocity of the bullet = 900 m/s The final momentum of the system is the sum of the rifle's momentum and the bullet's momentum: \(latex p_{final} = m_r v_r + m_b v_b\) 3. **Conservation of Momentum Equation:** Since momentum is conserved: \(latex p_{initial} = p_{final}\) \(latex 0 = m_r v_r + m_b v_b\) 4. **Solving for the Recoil Velocity (\(latex v_r\)):** Rearrange the equation to solve for \(latex v_r\): \(latex m_r v_r = -m_b v_b\) \(latex v_r = -\frac{m_b v_b}{m_r}\) 5. **Plugging in the Values:** \(latex v_r = -\frac{(0.0042 \, \text{kg})(900 \, \text{m/s})}{4.50 \, \text{kg}}\) \(latex v_r = -\frac{3.78}{4.50}\) \(latex v_r = -0.84 \, \text{m/s}\) **Answer** The recoil speed of the rifle is 0.84 m/s. The negative sign indicates that the rifle's recoil is in the opposite direction to the bullet's motion. 🎯