A particle is projected with speed \(u\) at an angle \(\alpha\) above the horizontal from a point \(O\) on a horizontal plane. The particle moves freely under gravity.
(a) Write down the horizontal and vertical components of the velocity of the particle at time \(T\) after projection.

At time \(T\) after projection, the direction of motion of the particle is perpendicular to the direction of projection.
(b) Express \(T\) in terms of \(u, g\) and \(\alpha\).
(c) Deduce that \(T\gt \frac{u}{g}\).