Halliday, Resnick & Walker — Center of Mass and Linear Momentum: Problem 61

61 Two bodies of masses \(m = 0.30 \text{ kg}\) and \(2m\) are connected by a long string of negligible mass. The string is looped over a pulley and, with the string taut, the bodies are released at time \(t = 0\) so that the heavier one descends and the lighter one ascends. At time \(t = 4.0 \text{ s}\), the lighter one undergoes a fully inelastic collision with a third body of mass \(m\). Because the first two bodies move in rigid fashion, the collision is effectively between the third body and the system of the first two bodies. (a) Just after the collision, what is the speed of the three bodies? (b) By how much was the kinetic energy of the descending body decreased because of the collision?