5 A particle \(P\) is projected with speed \(u \mathrm {~ms} ^ { - 1 }\) at an angle of \(\theta\) above the horizontal from a point \(O\) on a horizontal plane and moves freely under gravity. The horizontal and vertical displacements of \(P\) from \(O\) at a subsequent time \(t \mathrm {~s}\) are denoted by \(x \mathrm {~m}\) and \(y \mathrm {~m}\) respectively.

1. Starting from the equation of the trajectory given in the List of formulae (MF19), show that $$\mathrm { y } = \mathrm { x } \tan \theta - \frac { \mathrm { gx } ^ { 2 } } { 2 \mathrm { u } ^ { 2 } } \left( 1 + \tan ^ { 2 } \theta \right)$$ When \(\theta = \tan ^ { - 1 } 2 , P\) passes through the point with coordinates \(( 10,16 )\).
2. Show that there is no value of \(\theta\) for which \(P\) can pass through the point with coordinates \(( 18,30 )\).