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}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1829f362-1a16-45e8-8282-990908270dc7%2F2ff63e36-8ee0-4634-b698-2fe39dbed2e8%2F1mtw5j8_processed.png&w=3840&q=75)
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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