# Kinematics With Portals

**Classical Mechanics**Level 4

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 \(h\).

Give your answer in meters, rounded to 3 significant figures.

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