Kinematics With Portals

If you have never played the video game Portal, a portal is essentially a wormhole (or tunnel) which can teleport an object from one location to another instantaneously, almost as if the object had simply passed through a door. The portal will conserve kinetic energy and speed. However, the object's direction of travel will get shifted depending on how the portals are oriented relative to each other. In math-speak, the object's velocity vector relative to the first portal is equal to that same object's velocity vector relative to the second portal.

Now for the problem:

A ball is launched horizontally off of a ledge of height $$H$$ at an initial speed of $$V_o$$. Portal A (orange) is placed on the ground at a distance $$R$$ such that the ball will pass directly through the portal's center.

On a wall a distance $$\dfrac{R}{2}$$ away, Portal B (blue) is placed at a height $$h$$ such that, after the ball passes through, it will again fall into Portal A, but from the other side.

Note that the angle at which the ball falls into Portal A (relative to the ground) is the same as the angle at which the ball falls out of Portal B (relative to the wall).

Given that $$H = 6.00 \text{ m}$$ and $$V_o = 2.53\text{ m/s}$$, find $$h$$.

Take the acceleration due to gravity as $$g = 9.81 \text{ m/s}^2$$.