2. Particle \(A\) of mass \(2 m\) and particle \(B\) of mass \(k m\), where \(k\) is a positive constant, are moving towards each other in opposite directions along the same straight line on a smooth horizontal plane. The particles collide directly. Immediately before the collision the speed of \(A\) is \(u\) and the speed of \(B\) is \(3 u\). The direction of motion of each particle is reversed by the collision. Immediately after the collision the speed of \(A\) is \(\frac { 1 } { 2 } u\).

1. Show that \(k < 1\)
2. Find, in terms of \(m\) and \(u\), the magnitude of the impulse exerted on \(B\) by \(A\) in the collision.