7 In this question use \(g = 9.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
When a car, of mass 1200 kg , travels at a speed of \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) it experiences a total resistive force which can be modelled as being of magnitude \(36 v\) newtons.
The maximum power of the car is 90 kilowatts.
The car starts to descend a hill, inclined at \(5.2 ^ { \circ }\) to the horizontal, along a straight road.
Find the maximum speed of the car down this hill.
[0pt] [5 marks]