A particle \(P\) is projected with speed \(u \mathrm{~ms}^{-1}\) at an angle \(\theta\), where \(\tan \theta=2\), 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 time \(t \mathrm{~s}\) are denoted by \(x \mathrm{~m}\) and \(y \mathrm{~m}\) respectively. (a) Use the equation of the trajectory given in the list of formulae (MF 19) to show that \(y=2 x-\frac{25 x^{2}}{u^{2}}\) (b) In the subsequent motion, \(P\) passes through the point with coordinates \((8,12)\). The particle then hits a fixed vertical barrier 7 m high that is at a horizontal distance of \(D \mathrm{~m}\) from the point of projection.

Find the set of possible values of \(D\).