Two particles, $$\(P\)$$ and $$\(Q\)$$, with masses $$\(m\)$$ and $$\(2 m\)$$ respectively, are moving in the same direction along the same straight line when they collide directly. Immediately before they collide, $$\(P\)$$ is moving with speed $$\(4 u\)$$ and $$\(Q\)$$ is moving with speed $$\(u\)$$. Immediately after they collide, both particles are moving in the same direction and the speed of $$\(Q\)$$ is four times the speed of $$\(P\)$$. (a) Find the speed of $$\(Q\)$$ immediately after the collision. (3) (b) Find the magnitude of the impulse exerted by $$\(Q\)$$ on $$\(P\)$$ in the collision. (3) (c) State clearly the direction of this impulse. (1)

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