7.
\begin{figure}[h]
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\caption{Figure 3}
\includegraphics[alt={},max width=\textwidth]{7ae16b00-d388-4c1b-a195-c785a3900548-10_728_1210_303_376}
\end{figure}
A particle \(P\) is projected from a point \(A\) with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of elevation \(\theta\), where \(\cos \theta = \frac { 4 } { 5 }\). The point \(B\), on horizontal ground, is vertically below \(A\) and \(A B = 45 \mathrm {~m}\). After projection, \(P\) moves freely under gravity passing through a point \(C , 30 \mathrm {~m}\) above the ground, before striking the ground at the point \(D\), as shown in Figure 3.
Given that \(P\) passes through \(C\) with speed \(24.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\),
- using conservation of energy, or otherwise, show that \(u = 17.5\),
- find the size of the angle which the velocity of \(P\) makes with the horizontal as \(P\) passes through \(C\),
- find the distance \(B D\).