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Jimmy (60 kg) and Christine (52 kg) are both on roller skates facing each other. They push off each other and slide away in opposite directions. Christine moves with a speed of 1.2 m/s. What is Jimmy's speed? (momentum is conserved)|

Jimmy (60 kg) and Christine (52 kg) are both on roller skates facing each other. They push off each other and slide away in opposite directions. Christine moves with a speed of 1.2 m/s. What is Jimmy's speed? (momentum is conserved)|

College Physics
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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**Physics Problem: Conservation of Momentum** **Scenario:** Jimmy (60 kg) and Christine (52 kg) are both on roller skates facing each other. They push off each other and slide away in opposite directions. Christine moves with a speed of 1.2 m/s. **Question:** What is Jimmy's speed? (Assume momentum is conserved.) **Analysis:** This problem involves the principle of conservation of momentum. In an isolated system, the total momentum before an event must equal the total momentum after the event. **Solution:** Initially, both Jimmy and Christine are stationary, so the total initial momentum is zero. **Initial Momentum:** \[ P_{initial} = m_{Jimmy} \cdot v_{Jimmy} + m_{Christine} \cdot v_{Christine} \] \[ P_{initial} = 60 \, \text{kg} \cdot 0 \, \text{m/s} + 52 \, \text{kg} \cdot 0 \, \text{m/s} = 0 \] After they push off each other, Christine moves with a speed of 1.2 m/s in one direction. Let \( v_{Jimmy} \) be Jimmy's speed in the opposite direction. **Final Momentum:** \[ P_{final} = m_{Jimmy} \cdot v_{Jimmy} + m_{Christine} \cdot v_{Christine} \] Since they move in opposite directions, their velocities have opposite signs: \[ 0 = 60 \, \text{kg} \cdot v_{Jimmy} + 52 \, \text{kg} \cdot (-1.2 \, \text{m/s}) \] \[ 60 \, \text{kg} \cdot v_{Jimmy} = 52 \, \text{kg} \cdot 1.2 \, \text{m/s} \] \[ v_{Jimmy} = \frac{52 \, \text{kg} \cdot 1.2 \, \text{m/s}}{60 \, \text{kg}} \] \[ v_{Jimmy} = \frac{62.4 \, \text{kg} \cdot \text{m/s}}{60 \, \text{kg}} \] \[ v_{Jimmy} = 1.04 \, \text{
Transcribed Image Text:**Physics Problem: Conservation of Momentum** **Scenario:** Jimmy (60 kg) and Christine (52 kg) are both on roller skates facing each other. They push off each other and slide away in opposite directions. Christine moves with a speed of 1.2 m/s. **Question:** What is Jimmy's speed? (Assume momentum is conserved.) **Analysis:** This problem involves the principle of conservation of momentum. In an isolated system, the total momentum before an event must equal the total momentum after the event. **Solution:** Initially, both Jimmy and Christine are stationary, so the total initial momentum is zero. **Initial Momentum:** \[ P_{initial} = m_{Jimmy} \cdot v_{Jimmy} + m_{Christine} \cdot v_{Christine} \] \[ P_{initial} = 60 \, \text{kg} \cdot 0 \, \text{m/s} + 52 \, \text{kg} \cdot 0 \, \text{m/s} = 0 \] After they push off each other, Christine moves with a speed of 1.2 m/s in one direction. Let \( v_{Jimmy} \) be Jimmy's speed in the opposite direction. **Final Momentum:** \[ P_{final} = m_{Jimmy} \cdot v_{Jimmy} + m_{Christine} \cdot v_{Christine} \] Since they move in opposite directions, their velocities have opposite signs: \[ 0 = 60 \, \text{kg} \cdot v_{Jimmy} + 52 \, \text{kg} \cdot (-1.2 \, \text{m/s}) \] \[ 60 \, \text{kg} \cdot v_{Jimmy} = 52 \, \text{kg} \cdot 1.2 \, \text{m/s} \] \[ v_{Jimmy} = \frac{52 \, \text{kg} \cdot 1.2 \, \text{m/s}}{60 \, \text{kg}} \] \[ v_{Jimmy} = \frac{62.4 \, \text{kg} \cdot \text{m/s}}{60 \, \text{kg}} \] \[ v_{Jimmy} = 1.04 \, \text{
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