A car of mass 800 kg is moving at a constant speed of \(20 \mathrm {~ms} ^ { - 1 }\) on a straight road down a hill inclined at an angle \(\alpha\) to the horizontal. The engine of the car works at a constant rate of 10 kW and there is a resistance to motion of 1300 N . Show that \(\sin \alpha = \frac { 5 } { 49 }\).
The car now travels up the same hill and its engine now works at a constant rate of 20 kW . The resistance to motion remains 1300 N . The car starts from rest and its speed is \(8 \mathrm {~ms} ^ { - 1 }\) after it has travelled a distance of 22.1 m . Calculate the time taken by the car to travel this distance.