4 A car has a maximum speed of \(42 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) when it is moving on a horizontal road. When the speed of the car is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), it experiences a resistance force of magnitude \(30 v\) newtons.
- Show that the maximum power of the car is 52920 W .
- The car has mass 1200 kg . It travels, from rest, up a slope inclined at \(5 ^ { \circ }\) to the horizontal.
- Show that, when the car is travelling at its maximum speed \(\mathrm { V } \mathrm { m } \mathrm { s } ^ { - 1 }\) up the slope,
$$V ^ { 2 } + 392 \sin 5 ^ { \circ } V - 1764 = 0$$
- Hence find \(V\).