5. \begin{figure}[h] \end{figure} The points \(A\) and \(B\) lie 50 m apart on horizontal ground.
At time \(t = 0\) two small balls, \(P\) and \(Q\), are projected in the vertical plane containing \(A B\).
Ball \(P\) is projected from \(A\) with speed \(20 \mathrm {~ms} ^ { - 1 }\) at \(30 ^ { \circ }\) to \(A B\).
Ball \(Q\) is projected from \(B\) with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at angle \(\theta\) to \(B A\), as shown in Figure 3.
At time \(t = 2\) seconds, \(P\) and \(Q\) collide.
Until they collide, the balls are modelled as particles moving freely under gravity.

1. Find the velocity of \(P\) at the instant before it collides with \(Q\).
2. Find
   1. the size of angle \(\theta\),
   2. the value of \(u\).
3. State one limitation of the model, other than air resistance, that could affect the accuracy of your answers.