7.
\begin{figure}[h]
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\caption{Figure 4}
\includegraphics[alt={},max width=\textwidth]{a9e00b5b-3804-4f8d-9cc8-7d1170027726-6_568_1582_360_239}
\end{figure}
A particle \(P\) is projected from a point \(A\) with speed \(32 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of elevation \(\alpha\), where \(\sin \alpha = \frac { 3 } { 5 }\). The point \(O\) is on horizontal ground, with \(O\) vertically below \(A\) and \(O A = 20 \mathrm {~m}\). The particle \(P\) moves freely under gravity and passes through a point \(B\), which is 16 m above ground, before reaching the ground at the point \(C\), as shown in Figure 4.
Calculate
- the time of the flight from \(A\) to \(C\),
- the distance \(O C\),
- the speed of \(P\) at \(B\),
- the angle that the velocity of \(P\) at \(B\) makes with the horizontal.