7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{1822f86a-9089-44af-ab36-6006adfeb5b9-13_506_1379_287_280}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
At time \(t = 0\), a particle is projected from a fixed point \(O\) on horizontal ground with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle \(\theta ^ { \circ }\) to the horizontal. The particle moves freely under gravity and passes through the point \(A\) when \(t = 4 \mathrm {~s}\). As it passes through \(A\), the particle is moving upwards at \(20 ^ { \circ }\) to the horizontal with speed \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), as shown in Figure 3.
- Find the value of \(u\) and the value of \(\theta\).
At the point \(B\) on its path the particle is moving downwards at \(20 ^ { \circ }\) to the horizontal with speed \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
- Find the time taken for the particle to move from \(A\) to \(B\).
The particle reaches the ground at the point \(C\).
- Find the distance \(O C\).