7. The diagram below shows a particle \(P\), of mass \(2 \cdot 5 \mathrm {~kg}\), attached by means of two light inextensible strings fixed at points \(A\) and \(B\). Point \(A\) is vertically above point \(B\). \(B P\) makes an angle of \(60 ^ { \circ }\) with the upward vertical and \(A P\) is inclined at an angle \(\theta\) to the downward vertical where \(\cos \theta = 0 \cdot 8\). The particle \(P\) describes a horizontal circle with constant angular speed \(\omega\) radians per second about centre \(C\) with both strings taut.
\includegraphics[max width=\textwidth, alt={}, center]{2954c34b-dd8f-49a2-a379-704022574550-5_823_641_644_705} The tension in the string \(B P\) is \(39 \cdot 2 \mathrm {~N}\).

1. Calculate the tension in the string \(A P\).
2. Given that the length of the string \(A P\) is 1.5 m , find the value of \(\omega\).
3. Calculate the kinetic energy of \(P\).