A ship is anchored in the port. On its side there is a staircase with 10 steps visible over the water. Each step is 20 cm high. The tide rises at a rate of 15 cm per hour. How many hours will it take to cover 4 steps?
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The boat and the ladder
Hints
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- The boat is NOT anchored to the bottom. It floats freely on water following Archimedes' principle.
- Many people calculate: 3 hours × 15 cm/hour = 45 cm.
- Many people calculate: 45 cm ÷ 20 cm/step = 2.25 steps.
Solution
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Answer: No additional steps will be covered. The visible steps remain constant.
Conceptual explanation:
Visual comparison:
Initial situation (low tide):
- Steps 5, 6, 7, 8 visible over the water
- The boat floats at the current water level
After 3 hours (high tide +45cm):
- Steps 5, 6, 7, 8 are still visible over the water
- The ship has risen along with the water
- The ladder went up with the ship
Key concept:
The boat is NOT anchored to the bottom. It floats freely on water following Archimedes' principle.
Physical analysis:
- Tide rises → Water level increases 15 cm/hour
- Water pushes boat → Buoyancy force increases
- Boat rises → It rises exactly 15 cm/hour
- Ladder fixed to the boat → The ladder rises with the boat
- Relative distance → Water-steps remains constant
The problem trap:
Many people calculate:
- 3 hours × 15 cm/hour = 45 cm
- 45 cm ÷ 20 cm/step = 2.25 steps
But this calculation assumes that the ladder is fixed to the dock or bottom, which it is not!
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