6 A particle \(P\) is projected with speed \(u\) at an angle \(\alpha\) 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 \(t\) are denoted by \(x\) and \(y\) respectively.

1. Derive the equation of the trajectory of \(P\) in the form $$\mathrm { y } = \mathrm { x } \tan \alpha - \frac { \mathrm { gx } ^ { 2 } } { 2 \mathrm { u } ^ { 2 } } \sec ^ { 2 } \alpha$$ During its flight, \(P\) must clear an obstacle of height \(h \mathrm {~m}\) that is at a horizontal distance of 32 m from the point of projection. When \(u = 40 \sqrt { 2 } \mathrm {~ms} ^ { - 1 } , P\) just clears the obstacle. When \(u = 40 \mathrm {~ms} ^ { - 1 } , P\) only achieves \(80 \%\) of the height required to clear the obstacle.
2. Find the two possible values of \(h\).