A 56-kg canoeist sits at rest at the back end of a 23-kg canoe. The canoe is at

Question

A 56-kg canoeist sits at rest at the back end of a 23-kg canoe. The canoe is at rest in the still water of a lake with its front end about 0.50 m from the dock. The canoeist realizes that she has left the paddle on the dock, so she carefully works her way to the front of 3.8-m canoe. Is she likely to be able to reach the dock from the front of the boat?

(Hint: We can treat the system of the canoe and canoeist as if it were isolated.)
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Explanation / Answer

since this is an isolated system, the center of mass of the system remains at the same place. so, if she moves forward, the canoe will move backwards so that the center of mass remains at the same place. assuming canoe moves d distance back from dock Xcm = postion of centre of mass as measured from dock Xcm(before moving) = Xcm(after moving) [(0.5+1.9)*23 + (0.5+3.8)*56]/(23+56) = [(0.5+1.9+d)*23 + (0.5+d)*56]/(23+56) => 296 = 83.2 + 79d => d = (296-83.2)/79 d = 2.69367 m => she is not likely to be able to reach the dock

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