7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3eb71ecb-fa88-4cca-a2b6-bcf11f1d689b-20_517_947_212_500}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
The fixed point \(A\) is 20 m vertically above the point \(O\) which is on horizontal ground. At time \(t = 0\), a particle \(P\) is projected from \(A\) with speed \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle \(\theta ^ { \circ }\) above the horizontal. The particle moves freely under gravity. At time \(t = 5\) seconds, \(P\) strikes the ground at the point \(B\), where \(O B = 40 \mathrm {~m}\), as shown in Figure 4.
- By considering energy, find the speed of \(P\) as it hits the ground at \(B\).
- Find the least speed of \(P\) as it moves from \(A\) to \(B\).
- Find the length of time for which the speed of \(P\) is more than \(10 \mathrm {~ms} ^ { - 1 }\).