(i)[3]
A lorry travels steadily at $5\,\text{m s}^{-1}$ up a hill that is inclined at an angle of $\theta$ to the horizontal, where $\sin\theta = 0.08$. At this speed, the magnitude of the resistance to motion on the lorry is $1500\,\text{N}$. Show that the power of the lorry’s engine is $55.5\,\text{kW}$.
(ii)[1]
When the lorry moves at a speed of $v\,\text{m s}^{-1}$, the magnitude of the resistance to motion is $kv^2\,\text{N}$, where $k$ is a constant. Show that $k = 60$.
(iii)[3]
The lorry now travels at constant speed on a straight level road. If its engine is still delivering $55.5\,\text{kW}$, determine the lorry’s speed.