3. A car of mass 1200 kg experiences a resistance to motion, \(R\) newtons, which is proportional to its speed, \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\). When the power output of the car engine is 90 kW and the car is travelling along a horizontal road, its maximum speed is \(50 \mathrm {~ms} ^ { - 1 }\).

1. Show that \(R = 36 v\). The car ascends a hill inclined at an angle \(\theta\) to the horizontal where \(\sin \theta = \frac { 1 } { 14 }\).
2. Find, correct to 3 significant figures, the maximum speed of the car up the hill assuming that the power output of the engine is unchanged.
   (6 marks)