7.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{1822f86a-9089-44af-ab36-6006adfeb5b9-13_506_1379_287_280}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\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.
\begin{enumerate}[label=(\alph*)]
\item 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 $15 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\item Find the time taken for the particle to move from $A$ to $B$.

The particle reaches the ground at the point $C$.
\item Find the distance $O C$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2015 Q7 [12]}}