Your friend (mass of 141.1 kg) is canoeing on a lake with his sister (mass of 81

Question

Your friend (mass of 141.1 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 121 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

Assume thay both of them move at the same speed when trading
m1=mass of the brother
m2=mass of the sister
let v=v=speed they moves

Conservation of momentum
m1v1 - m2v2 + (m1+m2+mcanoe)vcanoe = 0
141.1v- 81.6v + (141.1+81.6+48.7)vcanoe = 0
vcanoe = -0.219v

( Canoe move to the direction opposite to the brother's direction, so it comes closer to the paddle)

vcanoe = distance canoe move / time        (1)

v = distance the brother move / time        (2)

both time are the same, so (1)/(2) => vcanoe / v = distance canoe / distance brother

0.219 = distance canoe / 2.03

distance canoe move = 0.445 m ( closer to the paddle )

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