Problem 1.154

Two identical buggies 1 and 2 with one man in each move without friction due to inertia along the parallel rails toward each other. When the buggies got opposite each other, the men exchange their places by jumping in the direction perpendicular to the motion direction. As a consequence, buggy 1 stops and buggy 2 keeps moving in the same direction, with its velocity becoming equal to \(\mathrm{v}\). Find the initial velocities of the buggies \(v_{1}\) and \(v_{2}\) if the mass of each buggy (without a man) equals \(M\) and the mass of each man m