Please explain **Physics Problem: Recoil Speed Calculation***A 100-kg machine gun fires a 0.5-kg bullet with a velocity of 400 m/s relative to the ground. What is the recoil speed of the machine gun?***Answer Options:**- 2.0 m/s- 20 m/s- 1.0 m/s- 4.0 m/s- 6.0 m/sThis question requires understanding of the law of conservation of momentum, which states that the total momentum before an event must equal the total momentum after the event in an isolated system.**To solve:**1. **Calculate the momentum of the bullet:** \[ p_{\text{bullet}} = m_{\text{bullet}} \times v_{\text{bullet}} = 0.5 \, \text{kg} \times 400 \, \text{m/s} = 200 \, \text{kg}\cdot\text{m/s} \]2. **Equate the momentum of the system before and after the gun fires (initially the system is at rest, so total initial momentum is 0):** \[ 0 = m_{\text{bullet}} \times v_{\text{bullet}} + m_{\text{gun}} \times v_{\text{gun}} \]3. **Rearrange to solve for the velocity of the gun \( v_{\text{gun}} \):** \[ v_{\text{gun}} = -\frac{m_{\text{bullet}} \times v_{\text{bullet}}}{m_{\text{gun}}} \] \[ v_{\text{gun}} = -\frac{200 \, \text{kg}\cdot\text{m/s}}{100 \, \text{kg}} = -2.0 \, \text{m/s} \]The negative sign indicates the direction of the recoil is opposite to the bullet's velocity. Hence, the recoil speed of the machine gun is **2.0 m/s**.

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Answered: A 100-kg machine gun fires a 0.5-kg…

A 100-kg machine gun fires a 0.5-kg bullet with a velocity of 400 m/s relative to the ground. What is the recoil speed of the machine gun? 2.0 m/s 20 m/s 1.0 m/s 4.0 m/s 6.0 m/s

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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