Edexcel M2 2017 June — Question 6

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2017
SessionJune
TopicProjectiles

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.
  1. Find
    1. the size of angle \(\theta\),
    2. the value of \(q\).
  2. Find the speed of \(P\) at the instant before it collides with \(Q\).