A man whose mass is 75 kg and a woman whose mass is 52 kg sit at opposite ends o

Question

A man whose mass is 75 kg and a woman whose mass is 52 kg sit at opposite ends of a canoe 5 m long, whose mass is 23 kg.

Relative to the man, where is the center of mass of the system consisting of man, woman, and canoe?
Distance of center of mass from left end of boat =

Suppose that the man moves quickly to the center of the canoe and sits down there. How far does the canoe move in the water? It helps a great deal to draw a diagram of the situation before and after the move.

Distance the boat moves =

Explanation / Answer

Say man is sitting on left end x1= 0 , x2 = 2.5, x3 = 5, M1= 75, m2 = 23 , M3 = 52 COM = M1 x1 + M2 * X2 + M3* X3 /(m1+ m2+ m3) = 75x0+ 23* 2.5+ 52* 5 /(75+23+52) = 2.1166 m from left end when he sits at the center of canoe x1= 2.5 m, x2= 2.5 , X3 = 5, M1= 75, m2 = 23 , M3 = 52 COM = M1 x1 + M2 * X2 + M3* X3 /(m1+ m2+ m3) we get = COM = 505/150 = 3.3666m hence distance the boat moves = - (displacement of COM) = -(3.3666-2.1166) = -1.25 m => boat moves left by 1.25 meters

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