Relative motion

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),



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