1. A car of mass 900 kg is moving on a straight road that is inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 1 } { 49 }\). When the car is moving up the road, with the engine of the car working at a constant rate of 10.8 kW , the car has a constant speed of \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The resistance to the motion of the car from non-gravitational forces is modelled as a constant force of magnitude \(R\) newtons.

When the car is moving down the road, with the engine of the car working at a constant rate of 10.8 kW , the car has a constant speed of \(2 v \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The resistance to the motion of the car is still modelled as a constant force of magnitude \(R\) newtons. Find

1. the value of \(R\),
2. the value of \(v\).