A particle P has mass 3m and a particle Q has mass 5m. The particles are moving towards each other in opposite directions along the same straight line on a smooth horizontal surface. The particles collide directly. Immediately before the collision, the speed of P is ku, where k is a constant, and the speed of Q is 2u. Immediately after the collision, the speed of P is u and the speed of Q is 3u. The direction of motion of Q is reversed by the collision.
(a) Find, in terms of m and u, the magnitude of the impulse exerted on Q by P in the collision. (I got 25mu here)
(b) Find the two possible values of k.