Particle $$\(A\)$$ of mass $$\(3 m\)$$ is moving in a straight line with speed $$\(2 u\)$$ on a smooth horizontal surface. Particle $$\(A\)$$ collides directly with particle $$\(B\)$$ of mass $$\(m\)$$, which is moving along the same straight line and in the same direction as $$\(A\)$$. Immediately before the collision, the speed of $$\(B\)$$ is $$\(u\)$$. As a result of the collision, the direction of motion of $$\(B\)$$ is unchanged and the kinetic energy gained by $$\(B\)$$ is $$\(\frac{48}{25} m u^{2}\)$$ (a) Find the coefficient of restitution between $$\(A\)$$ and $$\(B\)$$. (8) After the collision, $$\(B\)$$ hits a smooth fixed vertical wall that is perpendicular to the direction of motion of $$\(B\)$$. The coefficient of restitution between $$\(B\)$$ and the wall is $$\(f\)$$. Given that the speed of $$\(B\)$$ immediately after first hitting the wall is equal to the speed of $$\(A\)$$ immediately after its first collision with $$\(B\)$$, (b) find the value of $$\(f\)$$. (2)

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