Two smooth spheres of equal size are resting on a smooth, horizontal surface. Particle P, of mass m, is projected towards particle Q, of mass 2m, with velocity 3u. Particle Q is initially at rest. The coefficient of restitution between the spheres is e.

a. Show that particle P has its direction changed provided e > ½.

b. Given that the kinetic energy after the collision is half the initial kinetic energy, find the value of e and state the velocity of P.