6.
\begin{figure}[h]
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\caption{Figure 2}
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\end{figure}
A particle is at the highest point \(A\) on the outer surface of a fixed smooth sphere of radius \(a\) and centre \(O\). The lowest point \(B\) of the sphere is fixed to a horizontal plane. The particle is projected horizontally from \(A\) with speed \(u\), where \(u < \sqrt { } ( a g )\). The particle leaves the sphere at the point \(C\), where \(O C\) makes an angle \(\theta\) with the upward vertical, as shown in Fig. 2.
- Find an expression for \(\cos \theta\) in terms of \(u , g\) and \(a\).
The particle strikes the plane with speed \(\sqrt { \left( \frac { 9 a g } { 2 } \right) }\).
- Find, to the nearest degree, the value of \(\theta\).