Displacement of a Boat – Rankers Physics
Topic: Center of Mass , Momentum and Collision
Subtopic: Motion of Center of Mass

Displacement of a Boat

A boat of length \( 12\text{ m} \) and mass \( 840\text{ kg} \) is floating without motion in still water. A man of mass \( 60\text{ kg} \) standing at one end of it walks to the other end of it and stops. The magnitude of displacement of the boat relative to the ground is:
\( 50\text{ cm} \)
\( 80\text{ cm} \)
\( 120\text{ cm} \)
\( 150\text{ cm} \)

Solution:

Since no external horizontal force acts on the boat-man system, the center of mass does not move. The displacement of the boat is \( x = \frac{m L}{m + M} = \frac{60 \times 12}{60 + 840} = 0.8\text{ m} = 80\text{ cm} \).

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