Irodov Solution 1.159

Say initially the person is standing at position A on the raft. Let C be the center of the raft. Let CA = x0. Suppose that C is located at origin before the man started walking on the raft. The CG of the (raft + man) system will be located at O, where CO =
.

Now say the man moves l' units to the left on the raft. Since there are no external forces on the (raft+man) system, center of mass of the (raft+man) system will remain at the same location O even after the man walks on the raft. In order for the center of mass of the (raft+man) system to remain unchanged, if the man walks to the left, the raft must move to the right.
Suppose that the raft moves y units to the right.

This means that the final location of the man in an absolute reference frame will be x0-l'+y as shown in the figure. The center of mass of the (raft + man) system after the man moved will then be,






Since, the direction of y is in the opposite direction of that of l', in vectorial notation, the displacement of the raft is -y.

b) Differentiating (1) we have,




The momentum of the raft is thus given by . The force exerted by the man on the raft is the rate of change of momentum of the raft given by .