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. a) Find T in terms of u and g. 2 U b) Show that H = 2g c) The point A is at a height 3H 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.