Your friend (mass of 144.2 kg) is canoeing on a lake with his sister (mass of 81

Question

                     Your friend (mass of 144.2  kg) is canoeing on a lake with his sister (mass of                 

                    81.6 kg). He had the only paddle but managed to drop it in the lake. It has drifted just                 

                    out of his reach along the long axis of the canoe. His sister has taken physics and                 

                    suggests that if they trade places she might be able to reach the paddle. Due to the high                 

                    "slime" content of the lake and the surface of the canoe, the canoe moves in the water                 

                    without any friction or drag. The passengers sit 2.03 meters apart and the canoe has a                 

                    mass of 48.7 kg. After the passengers switch places, how much closer (m) to the paddle                 

                    (which does not move) is the end of the canoe?                 

Explanation / Answer

assuming the distance between the canoe and paddle=x

==> displacement of cahoe=x

and displacement of friend (mass of 144.2  kg)=2.03-x

and displacement of sister (mass of 81.6 kg)=2.03 +x

by conserving momentum

48.7*x -144.2*(2.03-x) +81.6*(2.03+x)=0

==> x=127.08/(48.7+144.2+81.6)=0.4629 m

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