Projectile motion in inclined planes?

[somnambulist]

Two inclined planes intersect in a horizontal plane. Their inclination to the horizontal is α and β. If a particle is projected at right angles to the former from a point in it so as to strike the other at right angles, then find the velocity of projection. Assume that the particle undergoes a vertical displacement of 'h' during its motion.

 

[Kurdt]

An attempt at the solution is required before any help can be given. A diagram might be nice as well.