4 A car has mass 1400 kg . When the speed of the car is \(v \mathrm {~ms} ^ { - 1 }\) the magnitude of the resistance to motion is \(\mathrm { kv } ^ { 2 } \mathrm {~N}\) where \(k\) is a constant.

1. The car moves at a constant speed of \(24 \mathrm {~ms} ^ { - 1 }\) up a hill inclined at an angle of \(\alpha\) to the horizontal where \(\sin \alpha = 0.12\). At this speed the magnitude of the resistance to motion is 480 N .
   1. Find the value of \(k\).
   2. Find the power of the car's engine.
2. The car now moves at a constant speed on a straight level road. Given that its engine is working at 54 kW , find this speed.
   \includegraphics[max width=\textwidth, alt={}, center]{3eaf3652-ff91-4bae-9f20-83487d635612-06_542_923_251_571} A particle of mass 0.8 kg lies on a rough plane which is inclined at an angle of \(28 ^ { \circ }\) to the horizontal. The particle is kept in equilibrium by a force of magnitude \(T \mathrm {~N}\). This force acts at an angle of \(35 ^ { \circ }\) above a line of greatest slope of the plane (see diagram). The coefficient of friction between the particle and the plane is 0.2 . Find the least and greatest possible values of \(T\).