Question

An 80 kg boat that is 9.6 m in length is initially 7.6 m from the pier. A 46 kg child stands at the end of the boat closest to the pier. The child then notices a turtle on a rock at the far end of the boat and proceeds to walk to the far end of the boat to observe the turtle. How far is the child from the pier when she reaches the far end of the boat?

Answer 1

13.695 m

Explanation:

The assumption made here is that the boat/water interface is essentially frictionless, so that the center of mass of the system remains in the same place as the occupant of the boat moves around.

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We can find the sum of the moments of boat and child about the pier end:

(46 kg)(7.6 m) + (80 kg)((7.6 +9.6/2) m) = 1341.6 kg·m

After the child moves, the center of mass of boat and child is presumed to remain in the same place. If x is the new distance from the pier to the child, the sum of moments is now ...

46x +80(x-4.8)* = 1341.6

126x -384 = 1341.6

x = (1341.6 +384)/126 = 13 73/105 ≈ 13.695 . . . meters

The child is about 13.695 meters from the pier when she reaches the far end of the boat.

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* The center of mass of the boat alone is half its length closer to the pier than is the child, so is located at x-4.8 meters.