Problems

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\(AOB\) represents a smooth vertical wall and \(XY\) represents a parallel smooth vertical barrier, both standing on a smooth horizontal table. A particle \(P\) is projected along the table from \(O\) with speed \(V\) in a direction perpendicular to the wall. At the time of projection, the distance between the wall and the barrier is \((75/32)VT\), where \(T\) is a constant. The barrier moves directly towards the wall, remaining parallel to the wall, with initial speed \(4V\) and with constant acceleration \(4V/T\) directly away from the wall. The particle strikes the barrier \(XY\) and rebounds. Show that this impact takes place at time \(5T/8\). The barrier is sufficiently massive for its motion to be unaffected by the impact. Given that the coefficient of restitution is \(1/2\), find the speed of \(P\) immediately after impact. \(P\) strikes \(AB\) and rebounds. Given that the coefficient of restitution for this collision is also \(1/2,\) show that the next collision of \(P\) with the barrier is at time \(9T/8\) from the start of the motion.