Try this problem useful for Physics Olympiad based on Relative motion.

The Problem: Relative motion Problem

A 40kg boy is standing on a plank of mass 160Kg. The plank originally at rest, is free to slide on a smooth frozen lake. The boy walks along the plank at a constant speed of 1.5m/s relative to the plank. What is the speed of the boy relative to the ice surface?


Let the mass of the boy be (m_b) and that of the plank be (m_p). Let us consider the velocity of the boy with respect to the ice be (v_i), that of the plank with respect to ice be (v_i) and that of the boy with respect to the plank is (v_{bp}).
Now, using conservation of momentum,
From equation (i),