Particle \(P\) of mass \(m\) and particle \(Q\) of mass \(k m\) are moving in opposite directions on a smooth horizontal plane when they collide directly. Immediately before the collision the speed of \(P\) is \(5 u\) and the speed of \(Q\) is \(u\). Immediately after the collision the speed of each particle is halved and the direction of motion of each particle is reversed.
Find
the value of \(k\),
the magnitude of the impulse exerted on \(P\) by \(Q\) in the collision.