6.
\begin{figure}[h]
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\caption{Figure 3}
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\end{figure}
Figure 3 represents the path of a skier of mass 70 kg moving on a ski-slope \(A B C D\). The path lies in a vertical plane. From \(A\) to \(B\), the path is modelled as a straight line inclined at \(60 ^ { \circ }\) to the horizontal. From \(B\) to \(D\), the path is modelled as an arc of a vertical circle of radius 50 m . The lowest point of the \(\operatorname { arc } B D\) is \(C\).
At \(B\), the skier is moving downwards with speed \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). At \(D\), the path is inclined at \(30 ^ { \circ }\) to the horizontal and the skier is moving upwards. By modelling the slope as smooth and the skier as a particle, find
- the speed of the skier at \(C\),
- the normal reaction of the slope on the skier at \(C\),
- the speed of the skier at \(D\),
- the change in the normal reaction of the slope on the skier as she passes \(B\).
The model is refined to allow for the influence of friction on the motion of the skier.
- State briefly, with a reason, how the answer to part (b) would be affected by using such a model. (No further calculations are expected.)