Three people A B and C with weights 120 lb 180 lb and 160 lb

Three people, A, B, and C, with weights 120 lb, 180 lb, and 160 lb, respectively, are sitting in a boat. The boat weights 300 lb, with its weight evenly distributed and it is moving at l mi/hr = V. The initial position of the people is The people move to new positions as shown: Find the distance of the boat to the position where it would have been if the people did not move

Solution

Let us take the left most point as origin (0,0)

the coordinate of 120 lb = (2,0) 180 lb =( 8,0) 160 lb = (16,0) and the weight of the boat 300 ln = centre of mass of the boat only = (8,0 )

so we find the centre of mass of boat + mass =( 120 x2 + 180 x 8 + 300 x 8+ 160 x 16 ) / (120 + 180 + 300 + 160)

= 8.74 cm

let us assume the boat + mass system shifts to the rght by x cm

so according to the problem coordinate of 180 lb = (4+x , 0)

coordinate of weight of boat (300 lb) = (8 + x , 0)

coordinate of 160 lb = ( 10+x , 0)

coordinate of 120 lb = (14 + x , 0)

centre of mass of the system = (180 ( 4+x) + 300 (8 +x) + 160(10 +x) +120 ( 14+x)) / 760 = 8.42 + x

now since there is no external force applied ,position of Centre of mass is constant

8.42 + x = 8.74 => x = 0.32 cm