A 400 kg woman and a 200 kg boy are sitting on a 500 kg cano

A 40.0 kg woman and a 20.0 kg boy are sitting on a 50.0 kg canoe 5.00 m long. The canoe
is floating freely on a calm lake. Initially, the boat is not moving. The woman is sitting 1.00 m from the front end of the canoe and the boy is sitting 1.00 m from the tail end of the canoe.Ignoring resistance to motion of the canoe in the water, how far does the canoe move if the woman and the boy switch places?

Solution

center of mass of the system is at [25*1+45*4 +60*2.5]/[25+45+60] = 2.730769231 m from the tail

Center of mass when they exchange places = [45*1+25*4 +60*2.5]/[25+45+60] =2.269230769 m from the tail.

So the canoe should move 2.730769231-2.269230769m = 0.461538462 m

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