Two persons, each of mass m , are standing at the two extremes of a railroad car of mass M resting on a smooth track, as shown in the figure. The person on the left jumps to the left with a horizontal speed u relative to the state of the car before the jump. Subsequently, the other person jumps to the right, again with the same horizontal speed u relative to the state of the car before his jump. Determine the velocit

Step-by-step solution

Let the right direction be taken as positive. Initially, the system (car and two persons) is at rest, so the initial momentum is zero. When the first person jumps to the left with speed u relative to the initial state of the car (which is at rest), his velocity with respect to the ground is -u . Let V₁ be the velocity of the car and the second person after the first jump. Applying conservation of linear momentum: 0 = m(-u) + (M + m)V₁ V₁ = mu M + m The second person then jumps to the right with speed u relative to