A particle $$\(P\)$$ has mass $$\(k m\)$$ and a particle $$\(Q\)$$ has mass $$\(m\)$$. The particles are moving towards each other in opposite directions along the same straight line when they collide directly. Immediately before the collision, $$\(P\)$$ has speed $$\(3 u\)$$ and $$\(Q\)$$ has speed $$\(u\)$$. As a result of the collision, the direction of motion of each particle is reversed and the speed of each particle is halved. (a) Find the value of $$\(k\)$$. (4) (b) Find, in terms of $$\(m\)$$ and $$\(u\)$$, the magnitude of the impulse exerted on $$\(Q\)$$ in the collision. (3)

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