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\includegraphics[max width=\textwidth, alt={}, center]{833c338f-53c1-436e-a772-0cdaf17fa72d-2_547_811_625_667} A uniform sphere \(P\) of mass \(m\) is at rest on a smooth horizontal table. The sphere is projected along the table with speed \(u\) and strikes a smooth vertical barrier \(A\) at an acute angle \(\alpha\). It then strikes another smooth vertical barrier \(B\) which is at right angles to \(A\) (see diagram). The coefficient of restitution between \(P\) and each of the barriers is \(e\). Show that the final direction of motion of \(P\) makes an angle \(\frac { 1 } { 2 } \pi - \alpha\) with the barrier \(B\) and find the total loss in kinetic energy as a result of the two impacts. [7]