How Far Does the Canoe Recoil When I Walk from One End to the Other?

AI Thread Summary
The discussion centers on calculating the recoil of a canoe when a person walks from one end to the other. The problem involves understanding the shift in the center of mass of the system, which includes both the person and the canoe. The initial center of mass is calculated using the formula Xcm = (Mc*L/2)/(M + Mc), while the new position after walking is represented as X'cm = [M*L + Mc*(L/2 - x)]. By applying the principle of conservation of momentum, it is established that the two center of mass positions must be equal, leading to the equation Xcm = X'cm. The final step involves solving for the distance x, which represents how far the canoe recoils.
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I am floating in a canoe in still water. I carefully walk from one end of the canoe to the other. If my mass is M and the canoe's is Mc, how far does the canoe recoil?

I've solved more complicated problems but this one confuses me. Isn't recoil the velocity of a body after collision? I would have thought I would need at least one velocity. Obviously the center of mass shifts from end of the canoe to the other. I'm confused on how to approach this problem.
 
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If you measure the distance of the center of mass from the end from which you have started walking, and L is the length of the canoe, the center of mass of you and canoe before you start walking is

Xcm = (Mc*L/2)/(M + Mc)

When you move to the other end of the canoe, the center of mass will be

X'cm = [M*L + Mc*(L/2 - x)]

Since there is no external force acting on the canoe Xcm = X'cm.

Now solve for x.
 

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