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The boat and the ladder

Visual trapsLevel 1 · Starter · ●○○○○

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?

Hints

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  1. The boat is NOT anchored to the bottom. It floats freely on water following Archimedes' principle.
  2. Many people calculate: 3 hours × 15 cm/hour = 45 cm.
  3. 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.
The boat rises with the tide: the same section of the ladder remains visible
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:

  1. Tide rises → Water level increases 15 cm/hour
  2. Water pushes boat → Buoyancy force increases
  3. Boat rises → It rises exactly 15 cm/hour
  4. Ladder fixed to the boat → The ladder rises with the boat
  5. 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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