6
\includegraphics[max width=\textwidth, alt={}, center]{28562a1b-ec9a-40d2-bbb3-729770688971-3_218_1280_1146_431}
\(A B\) and \(B C\) are straight roads inclined at \(5 ^ { \circ }\) to the horizontal and \(1 ^ { \circ }\) to the horizontal respectively. \(A\) and \(C\) are at the same horizontal level and \(B\) is 45 m above the level of \(A\) and \(C\) (see diagram, which is not to scale). A car of mass 1200 kg travels from \(A\) to \(C\) passing through \(B\).

1. For the motion from \(A\) to \(B\), the speed of the car is constant and the work done against the resistance to motion is 360 kJ . Find the work done by the car's engine from \(A\) to \(B\). The resistance to motion is constant throughout the whole journey.
2. For the motion from \(B\) to \(C\) the work done by the driving force is 1660 kJ . Given that the speed of the car at \(B\) is \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), show that its speed at \(C\) is \(29.9 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), correct to 3 significant figures.
3. The car's driving force immediately after leaving \(B\) is 1.5 times the driving force immediately before reaching \(C\). Find, correct to 2 significant figures, the ratio of the power developed by the car's engine immediately after leaving \(B\) to the power developed immediately before reaching \(C\).