To find the average velocity and average speed of both Jack and Jill, we'll use their swimming distances and total time.
Jack's Average Speed and Velocity
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Distance Swum by Jack:
- Length of pool = 25.0 m
- Number of lengths = 9 \[ \text{Total distance} = 9 \text{ lengths} \times 25.0 \text{ m/length} = 225.0 \text{ m} \]
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Time Taken by Jack:
- Time = 162.5 s
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Average Speed of Jack: \[ \text{Average speed} = \frac{\text{Total distance}}{\text{Time}} = \frac{225.0 \text{ m}}{162.5 \text{ s}} \approx 1.38 \text{ m/s} \]
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Average Velocity of Jack:
- Since he swims back and forth in the pool, his displacement (the distance from the start point to the end point) is the same as the distance swum in one length.
- For 9 lengths, if he returns to the start point, the total displacement is 0 m. \[ \text{Average velocity} = \frac{\text{Displacement}}{\text{Time}} = \frac{0 \text{ m}}{162.5 \text{ s}} = 0 \text{ m/s} \]
Jill's Average Speed and Velocity
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Distance Swum by Jill:
- Length of pool = 25.0 m
- Number of lengths = 10 \[ \text{Total distance} = 10 \text{ lengths} \times 25.0 \text{ m/length} = 250.0 \text{ m} \]
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Time Taken by Jill:
- Time = 162.5 s (same as Jack)
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Average Speed of Jill: \[ \text{Average speed} = \frac{\text{Total distance}}{\text{Time}} = \frac{250.0 \text{ m}}{162.5 \text{ s}} \approx 1.54 \text{ m/s} \]
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Average Velocity of Jill:
- Similar to Jack, Jill's displacement is also based on her initial and final positions. Assuming she finishes at the 10th length without returning, her displacement would be:
- Total displacement = 10 lengths (from start to finish, not backtracking) = 250.0 m. \[ \text{Average velocity} = \frac{\text{Displacement}}{\text{Time}} = \frac{250.0 \text{ m}}{162.5 \text{ s}} \approx 1.54 \text{ m/s} \]
Summary
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Jack:
- Average Speed: \( \approx 1.38 \text{ m/s} \)
- Average Velocity: \( 0 \text{ m/s} \)
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Jill:
- Average Speed: \( \approx 1.54 \text{ m/s} \)
- Average Velocity: \( \approx 1.54 \text{ m/s} \)
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