Take \(g=10\,\mathrm{m\,s^{-2}}\). A 1400 kg car experiences resistance \(kv^2\) N at speed \(v\,\mathrm{m\,s^{-1}}\). It moves steadily at \(24\,\mathrm{m\,s^{-1}}\) up a hill with \(\sin\alpha=0.12\). At this speed resistance is 480 N.

(a)(i) Find k. [1]

(a)(ii) Find the engine power. [3]

(b) The car now moves steadily on a level road with engine power 54 kW. Find its speed. [3]