At time \(t=0\), a particle \(P\) is projected with speed \(u\,\text{m s}^{-1}\) at an angle \(60^\circ\) above the horizontal from a point \(O\). It then moves freely under gravity.

The direction of motion of \(P\) when \(t=5\) is perpendicular to its direction of motion when \(t=15\).

Find \(u\).