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2. Bob and Linda are sweethearts that enjoy skating arm in arm. Bob has a mass of 85 kg and Linda has a mass of 60 kg. Initially Bob is standing still when Linda comes up behind him with a speed of 3.0 m/s. What is the couple's final speed? Before: After: V Li Vị

2. Bob and Linda are sweethearts that enjoy skating arm in arm. Bob has a mass of 85 kg and Linda has a mass of 60 kg. Initially Bob is standing still when Linda comes up behind him with a speed of 3.0 m/s. What is the couple's final speed? Before: After: V Li Vị

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### Momentum and Collisions: A Case Study on Bob and Linda **Scenario Description:** Bob and Linda are sweethearts who enjoy skating arm in arm. Bob has a mass of 85 kg, and Linda has a mass of 60 kg. Initially, Bob is standing still when Linda comes up from behind him with a speed of \( v_{Li} = 3.0 \, \text{m/s} \). We are tasked with finding the couple’s final speed after they join together. **Illustration Explanation:** The diagram is divided into two parts: 1. **Before:** - The first part shows Bob and Linda separately. Bob is stationary, represented by a standing figure with no speed indicated. - Linda is moving towards Bob from behind with an initial velocity \( v_{Li} \) of 3.0 m/s. - The arrows indicate the direction and the speed vector of Linda while Bob has no speed vector attached to him, indicating he is at rest. 2. **After:** - The second part illustrates the moment after Linda has caught up with Bob, and they are now skating together arm in arm. - Both Bob and Linda are shown moving together with the final speed \( v_i \), which is what we need to determine. - The directional arrow indicates their common direction of movement. **Question:** What is the couple’s final speed after Linda catches up to Bob? **Answering the Question:** To find the final speed, we apply the principle of conservation of momentum. The equation for conservation of momentum before and after Linda catches Bob is: \[ \text{Initial total momentum} = \text{Final total momentum} \] Initially: - Momentum of Bob: \( m_B \cdot v_{Bi} = 85 \, \text{kg} \cdot 0 \, \text{m/s} = 0 \) - Momentum of Linda: \( m_L \cdot v_{Li} = 60 \, \text{kg} \cdot 3.0 \, \text{m/s} = 180 \, \text{kg} \cdot \text{m/s} \) After they come together: - Combined mass: \( m_B + m_L = 85 \, \text{kg} + 60 \, \text{kg} = 145 \, \text{kg}
Transcribed Image Text:### Momentum and Collisions: A Case Study on Bob and Linda **Scenario Description:** Bob and Linda are sweethearts who enjoy skating arm in arm. Bob has a mass of 85 kg, and Linda has a mass of 60 kg. Initially, Bob is standing still when Linda comes up from behind him with a speed of \( v_{Li} = 3.0 \, \text{m/s} \). We are tasked with finding the couple’s final speed after they join together. **Illustration Explanation:** The diagram is divided into two parts: 1. **Before:** - The first part shows Bob and Linda separately. Bob is stationary, represented by a standing figure with no speed indicated. - Linda is moving towards Bob from behind with an initial velocity \( v_{Li} \) of 3.0 m/s. - The arrows indicate the direction and the speed vector of Linda while Bob has no speed vector attached to him, indicating he is at rest. 2. **After:** - The second part illustrates the moment after Linda has caught up with Bob, and they are now skating together arm in arm. - Both Bob and Linda are shown moving together with the final speed \( v_i \), which is what we need to determine. - The directional arrow indicates their common direction of movement. **Question:** What is the couple’s final speed after Linda catches up to Bob? **Answering the Question:** To find the final speed, we apply the principle of conservation of momentum. The equation for conservation of momentum before and after Linda catches Bob is: \[ \text{Initial total momentum} = \text{Final total momentum} \] Initially: - Momentum of Bob: \( m_B \cdot v_{Bi} = 85 \, \text{kg} \cdot 0 \, \text{m/s} = 0 \) - Momentum of Linda: \( m_L \cdot v_{Li} = 60 \, \text{kg} \cdot 3.0 \, \text{m/s} = 180 \, \text{kg} \cdot \text{m/s} \) After they come together: - Combined mass: \( m_B + m_L = 85 \, \text{kg} + 60 \, \text{kg} = 145 \, \text{kg}
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