The diagram shows the vertical cross-section $ABC$ of a fixed surface. $AB$ is a curve and $BC$ is a horizontal straight line. The part of the surface containing $AB$ is smooth and the part containing $BC$ is rough. $A$ is at a height of $1.8{\text{ }}m$ above $BC$. A particle of mass $0.5{\text{ }}kg$ is released from rest at $A$ and travels along the surface to $C$.
a) Find the speed of the particle at $B$.
b) Given that the particle reaches $C4$ with a speed of $5{\text{ }}m{\text{ }}{s^{ - 1}}$, find the work done against the resistance to motion as the particle moves from $B$ to $C$.

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