Question

A particle is projected vertically upwards from a point O with velocity u sure that if u^2 > 2gh, the particle is at a height h above O at times which are separated by [2(u^2-2gh)1/2]/g

Answer 1

The particle is at a height h above O can be seen as projectile from that point with:
u^'.
〖u^'〗^2=u^2-2gh.
u^'=√(u^2-2gh).
The time of flight of projectile is
t^'=(2u^')/g=(2√(u^2-2gh))/g