1. A particle \(A\) has mass \(2 m\) and a particle \(B\) has mass \(3 m\). The particles are moving in opposite directions along the same straight line and collide directly.

Immediately before the collision, the speed of \(A\) is \(2 u\) and the speed of \(B\) is \(u\). Immediately after the collision, the speed of \(A\) is \(0.5 u\) and the speed of \(B\) is \(w\). Given that the direction of motion of each particle is reversed by the collision,

1. find \(w\) in terms of \(u\)
2. find the coefficient of restitution between the particles,
3. find, in terms of \(m\) and \(u\), the magnitude of the impulse received by \(A\) in the collision.