7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c16c17b6-2c24-4939-b3b5-63cd63646b76-20_360_1026_246_466}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{figure}
At time \(t = 0\) a particle \(P\) is projected from a fixed point \(A\) on horizontal ground. The particle is projected with speed \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle \(\alpha\) to the ground. The particle moves freely under gravity. At time \(t = 3\) seconds, \(P\) is passing through the point \(B\) with speed \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and is moving downwards at an angle \(\beta\) to the horizontal, as shown in Figure 5.
- By considering energy, find the height of \(B\) above the ground.
- Find the size of angle \(\alpha\).
- Find the size of angle \(\beta\).
- Find the least speed of \(P\) as \(P\) travels from \(A\) to \(B\).
As \(P\) travels from \(A\) to \(B\), the speed, \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), of \(P\) is such that \(v \leqslant 15\) for an interval of \(T\) seconds.
- Find the value of \(T\).
\section*{\textbackslash section*\{Question 7 continued\}}