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

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SUMMARY

The discussion focuses on calculating the recoil distance of a canoe when a person walks from one end to the other. The key formula derived involves the center of mass (Xcm) of the system, which is expressed as Xcm = (Mc*L/2)/(M + Mc) before movement and X'cm = [M*L + Mc*(L/2 - x)] after movement. The principle of conservation of momentum is applied, stating that since no external forces act on the system, Xcm must equal X'cm. The solution for the recoil distance (x) is derived from this equality.

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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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