M2 June 2017 Q6

EdexcelOld spec11 marksProjectiles

6.

Figure 4: P projected from A at 30 m/s at 60 degrees to AB and Q projected from B at q m/s at angle theta to BA, AB = 40 m
Figure 4

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 \(AB\) and move freely under gravity. Particle \(P\) is projected from \(A\) with speed 30 m s\(^{-1}\) at 60\(^\circ\) to \(AB\) and particle \(Q\) is projected from \(B\) with speed \(q\) m s\(^{-1}\) at angle \(\theta\) to \(BA\), as shown in Figure 4.

At \(t = 2\) seconds, \(P\) and \(Q\) collide.

(a) Find
(i) the size of angle \(\theta\),
(ii) the value of \(q\). (6)
(b) Find the speed of \(P\) at the instant before it collides with \(Q\). (5)
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