6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{64b0abc9-4021-44e6-8bf7-1a5862617085-20_248_1063_260_443}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
The points \(A\) and \(B\) lie 40 m apart on horizontal ground. At time \(t = 0\) the particles \(P\) and \(Q\) are projected in the vertical plane containing \(A B\) and move freely under gravity. Particle \(P\) is projected from \(A\) with speed \(30 \mathrm {~ms} ^ { - 1 }\) at \(60 ^ { \circ }\) to \(A B\) and particle \(Q\) is projected from \(B\) with speed \(q \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at angle \(\theta\) to \(B A\), as shown in Figure 4.
At \(t = 2\) seconds, \(P\) and \(Q\) collide.
- Find
- the size of angle \(\theta\),
- the value of \(q\).
- Find the speed of \(P\) at the instant before it collides with \(Q\).