3 Two particles \(P\) and \(Q\) are projected simultaneously with speed \(40 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a point \(O\) on a horizontal plane. Both particles subsequently pass at different times through the point \(A\) which has horizontal and vertically upward displacements from \(O\) of 40 m and 15 m respectively.

1. By considering the equation of the trajectory of a projectile, show that each angle of projection satisfies the equation \(\tan ^ { 2 } \theta - 8 \tan \theta + 4 = 0\).
2. Calculate the distance between the points at which \(P\) and \(Q\) strike the plane.