8 A particle is launched from the point $A$ on a horizontal surface, with a velocity of $22.4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at an angle $\theta$ above the horizontal, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{828e8db1-efcf-4878-8292-ba5bbd80115c-5_369_1182_406_431}

After 2 seconds, the particle reaches the point $C$, where it is at its maximum height above the surface.
\begin{enumerate}[label=(\alph*)]
\item Show that $\sin \theta = 0.875$.
\item Find the height of the point $C$ above the horizontal surface.
\item The particle returns to the surface at the point $B$. Find the distance between $A$ and $B$. (3 marks)
\item Find the length of time during which the height of the particle above the surface is greater than 5 metres.
\item Find the minimum speed of the particle.
\end{enumerate}

\hfill \mbox{\textit{AQA M1 2012 Q8 [16]}}