At time \(t = 0\), a particle is projected vertically upwards with speed \(u\) from a point \(A\). The particle moves freely under gravity. At time \(T\) the particle is at its maximum height \(H\) above \(A\).
Find \(T\) in terms of \(u\) and \(g\).
Show that \(H = \frac { u ^ { 2 } } { 2 g }\)
The point \(A\) is at a height \(3 H\) above the ground.
Find, in terms of \(T\), the total time from the instant of projection to the instant when the particle hits the ground.