A particle $$\(A\)$$ has mass $$\(4 m\)$$ and a particle $$\(B\)$$ has mass $$\(3 m\)$$. The particles are moving along the same straight line on a smooth horizontal plane. They are moving in opposite directions towards each other and collide directly. Immediately before the collision the speed of $$\(A\)$$ is $$\(2 u\)$$ and the speed of $$\(B\)$$ is $$\(3 u\)$$. The direction of motion of each particle is reversed by the collision. The total kinetic energy lost in the collision is $$\(\frac{473}{24} m u^{2}\)$$ Find (i) the coefficient of restitution between $$\(A\)$$ and $$\(B\)$$, (ii) the magnitude of the impulse received by $$\(A\)$$ in the collision. (12)

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