- A car of mass 1000 kg moves with constant speed \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\) up a straight road inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 1 } { 30 }\). The engine of the car is working at a rate of 12 kW . The resistance to motion from non-gravitational forces has magnitude 500 N . Find the value of \(V\).
- A particle \(P\) of mass \(m\) is moving in a straight line on a smooth horizontal surface with speed \(4 u\). The particle \(P\) collides directly with a particle \(Q\) of mass \(3 m\) which is at rest on the surface. The coefficient of restitution between \(P\) and \(Q\) is \(e\). The direction of motion of \(P\) is reversed by the collision.
Show that \(e > \frac { 1 } { 3 }\).