2 A particle \(P\) is projected with speed \(26 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(30 ^ { \circ }\) above the horizontal from a point \(O\) on a horizontal plane.

1. For the instant when the vertical component of the velocity of \(P\) is \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) downwards, find the direction of motion of \(P\) and the height of \(P\) above the plane.
2. \(P\) strikes the plane at the point \(A\). Calculate the time taken by \(P\) to travel from \(O\) to \(A\) and the distance \(O A\).
   \includegraphics[max width=\textwidth, alt={}, center]{022776e2-80bb-4e73-a309-8cd972ae7377-2_679_455_1544_845} Particles \(P\) and \(Q\) have masses 0.8 kg and 0.4 kg respectively. \(P\) is attached to a fixed point \(A\) by a light inextensible string which is inclined at an angle \(\alpha ^ { \circ }\) to the vertical. \(Q\) is attached to a fixed point \(B\), which is vertically below \(A\), by a light inextensible string of length 0.3 m . The string \(B Q\) is horizontal. \(P\) and \(Q\) are joined to each other by a light inextensible string which is vertical. The particles rotate in horizontal circles of radius 0.3 m about the axis through \(A\) and \(B\) with constant angular speed \(5 \mathrm { rad } \mathrm { s } ^ { - 1 }\) (see diagram).
3. By considering the motion of \(Q\), find the tensions in the strings \(P Q\) and \(B Q\).
4. Find the tension in the string \(A P\) and the value of \(\alpha\).