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.

1. Show that \(\sin \theta = 0.875\).
2. Find the height of the point \(C\) above the horizontal surface.
3. The particle returns to the surface at the point \(B\). Find the distance between \(A\) and \(B\). (3 marks)
4. Find the length of time during which the height of the particle above the surface is greater than 5 metres.
5. Find the minimum speed of the particle.