Bob, whose mass is 90 kg, is out in a 4 meter long canoe that has a mass of 110

Question

Bob, whose mass is 90 kg, is out in a 4 meter long canoe that has a mass of 110 kg. Bob is sitting at the left end of the boat, which is 10 meters away from the shore. For reference, the shore is at x = 0. Suddenly Amy appears on the shore, yelling at Bob that she wants a tug-of-war rematch on solid ground. Bob, terrified of this threat, gets up and walks to the right end of the boat to pretend he didn't hear her. Given that the rowboat's center of mass is at its physical center (2 meters from each end), how far from the shore is the center of mass of the entire Bob-boat system initially?, Since there are no external forces on the system (we are neglecting the water resistance), the center of mass location cannot change. Use this fact to determine the distance between the left end of the boat and the shore now. Hint: you don't know either Bob's or the boat's position now, but you do know where they are relative to each other

Explanation / Answer

let the left end be at a distance x=d from the shore
then right end will be at x=d+4

and the center of the boat will be at x=d+2

now bob is at x=d+4

hence center of mass=[90*(d+4)+110*(d+2)]/(90+110)=(200*d+580)/200

as there is no external force on the system, the center of mass is not changed.

hence (200*d+580)/200=11.1

d=8.2 m

hene the left end of the boat is at a distance of 8.2 m from the shore.

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