All right, so: dog on a boat. It's the snoopy problem. There's a boat floating on some water, and there's a dog on the end - he starts at X away from the shore. Then, he walks a length L across the boat towards the shore. How far is he away from the shore at the end?
m1r1 + m2r2 = (m1 + m2)rcm
The Attempt at a Solution
As far as I can get is to set the center of mass as X at the beginning.
Mboat * Xi + Mdog * Xi = (Mboat + Mdog)Xi
and then the dog walks L towards the shore and I am not sure how to set this equation up.
Mboat * (Xi + L) + Mdog * (Xi - L) = (Mboat + Mdog) Xi
See, I know the center of mass doesn't move, because the system is isolated and the only forces are internal. However, I don't know how to make the positions relative - this equation would work if the problem literally stated he walks a length L towards the shore (his new position obviously would be Xi - L) but it says he walks length L down the boat, which means the boat moves too and he doesn't quite make the distance L from an external observer's point of view.