Two particles, \(A\) and \(B\), have masses \(2 m\) and \(3 m\) respectively. They are moving towards each other in opposite directions along the same straight line on a smooth horizontal plane when they collide directly. Immediately before they collide, the speed of \(A\) is \(3 u\) and the speed of \(B\) is \(u\). As a result of the collision, the speed of \(A\) is halved and the direction of motion of each particle is reversed.
Find the speed of \(B\) immediately after the collision.
Find the magnitude of the impulse exerted on \(A\) by \(B\) in the collision.