Use \(g=10\text{ m s}^{-2}\).

An 18000 kg lorry travels along a straight road.

(a) On a horizontal section the engine power is constant and resistance is 1600 N.

(a)(i) The steady speed at power \(P\text{ W}\) is \(30\text{ m s}^{-1}\). Find \(P\). [1]

(a)(ii) At speed \(16\text{ m s}^{-1}\), the engine power is 40 kW. Find the acceleration. [2]

(b) At speed \(20\text{ m s}^{-1}\) the lorry starts up a hill inclined at \(\alpha^\circ\). It ascends at unchanged speed with engine power 120 kW and resistance still 1600 N. Find \(\alpha\). [3]