5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f9dc8158-8ed8-4138-9c75-050cf52e6f7e-12_965_1226_244_422}
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\caption{Figure 2}
\end{figure}
A small ball is projected with speed \(28 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a point \(O\) on horizontal ground. After moving for \(T\) seconds, the ball passes through the point \(A\).
The point \(A\) is 40 m horizontally and 20 m vertically from the point \(O\), as shown in Figure 2.
The motion of the ball from \(O\) to \(A\) is modelled as that of a particle moving freely under gravity.
Given that the ball is projected at an angle \(\alpha\) to the ground, use the model to
- show that \(T = \frac { 10 } { 7 \cos \alpha }\)
- show that \(\tan ^ { 2 } \alpha - 4 \tan \alpha + 3 = 0\)
- find the greatest possible height, in metres, of the ball above the ground as the ball moves from \(O\) to \(A\).
The model does not include air resistance.
- State one other limitation of the model.