5 A cyclist is riding up a straight hill inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = 0.04\). The total mass of the bicycle and rider is 80 kg . The cyclist is riding at a constant speed of \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). There is a force resisting the motion. The work done by the cyclist against this resistance force over a distance of 25 m is 600 J .

1. Find the power output of the cyclist.
   The cyclist reaches the top of the hill, where the road becomes horizontal, with speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The cyclist continues to work at the same rate on the horizontal part of the road.
2. Find the speed of the cyclist 10 seconds after reaching the top of the hill, given that the work done by the cyclist during this period against the resistance force is 1200 J .
   \includegraphics[max width=\textwidth, alt={}, center]{d3bb18c3-8c6f-41d4-808e-479f0c92250f-08_346_616_260_762} Two particles \(P\) and \(Q\), each of mass \(m \mathrm {~kg}\), are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley which is attached to the edge of a rough plane. The plane is inclined at an angle \(\alpha\) to the horizontal, where \(\tan \alpha = \frac { 7 } { 24 }\). Particle \(P\) rests on the plane and particle \(Q\) hangs vertically, as shown in the diagram. The string between \(P\) and the pulley is parallel to a line of greatest slope of the plane. The system is in limiting equilibrium.