8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{80dceee7-2eea-4082-ad20-7b3fe4e8bb25-24_470_824_214_561}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
The fixed point \(A\) is \(h\) metres vertically above the point \(O\) that is on horizontal ground. At time \(t = 0\), a particle \(P\) is projected from \(A\) with speed \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The particle moves freely under gravity. At time \(t = 2.5\) seconds, \(P\) strikes the ground at the point \(B\). At the instant when \(P\) strikes the ground, the speed of \(P\) is \(18 \mathrm {~ms} ^ { - 1 }\), as shown in Figure 4.
- By considering energy, find the value of \(h\).
- Find the distance \(O B\).
As \(P\) moves from \(A\) to \(B\), the speed of \(P\) is less than or equal to \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) for \(T\) seconds.
- Find the value of \(T\)