5.
\begin{figure}[h]
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\caption{Figure 2}
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A small ball is projected with speed \(U \mathrm {~ms} ^ { - 1 }\) from a point \(O\) at the top of a vertical cliff. The point \(O\) is 25 m vertically above the point \(N\) which is on horizontal ground.
The ball is projected at an angle of \(45 ^ { \circ }\) above the horizontal.
The ball hits the ground at a point \(A\), where \(A N = 100 \mathrm {~m}\), as shown in Figure 2 .
The motion of the ball is modelled as that of a particle moving freely under gravity.
Using this initial model,
- show that \(U = 28\)
- find the greatest height of the ball above the horizontal ground \(N A\).
In a refinement to the model of the motion of the ball from \(O\) to \(A\), the effect of air resistance is included.
This refined model is used to find a new value of \(U\).
- How would this new value of \(U\) compare with 28, the value given in part (a)?
- State one further refinement to the model that would make the model more realistic.
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