3
\includegraphics[max width=\textwidth, alt={}, center]{fe5c198d-5d05-4241-98f5-894ba92f7afe-3_408_1164_248_493} A particle \(P\) is released from rest at a point \(A\) which is 7 m above horizontal ground. At the same instant that \(P\) is released a particle \(Q\) is projected from a point \(O\) on the ground. The horizontal distance of \(O\) from \(A\) is 24 m . Particle \(Q\) moves in the vertical plane containing \(O\) and \(A\), with initial speed \(50 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and initial direction making an angle \(\theta\) above the horizontal, where \(\tan \theta = \frac { 7 } { 24 }\) (see diagram). Show that the particles collide.