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

[uchicago2012]

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.

 

[rl.bhat]

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.