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\includegraphics[max width=\textwidth, alt={}, center]{af19f1e0-4cdf-407b-a0d6-cb0272066c30-3_165_1417_1320_365} A cyclist and his machine have a total mass of 80 kg . The cyclist starts from rest at the top \(A\) of a straight path \(A B\), and freewheels (moves without pedalling or braking) down the path to \(B\). The path \(A B\) is inclined at \(2.6 ^ { \circ }\) to the horizontal and is of length 250 m (see diagram).

1. Given that the cyclist passes through \(B\) with speed \(9 \mathrm {~ms} ^ { - 1 }\), find the gain in kinetic energy and the loss in potential energy of the cyclist and his machine. Hence find the work done against the resistance to motion of the cyclist and his machine. The cyclist continues to freewheel along a horizontal straight path \(B D\) until he reaches the point \(C\), where the distance \(B C\) is \(d \mathrm {~m}\). His speed at \(C\) is \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The resistance to motion is constant, and is the same on \(B D\) as on \(A B\).
2. Find the value of \(d\). The cyclist starts to pedal at \(C\), generating 425 W of power.
3. Find the acceleration of the cyclist immediately after passing through \(C\).