A smooth hemisphere of radius $R$ is fixed with its flat face on a horizontal floor, as shown in the figure. A small particle is placed at its top and given a horizontal speed $u = \sqrt{gR/2}$. The particle slides down the curved surface and, at some point, leaves it. How far below the top of the hemisphere is the particle when it loses contact?

Fig. 1: A smooth hemisphere of radius R fixed on the floor, with a small particle at its top given a horizontal speed u.