A Falling Rod's Intersection Moving Faster Than Light?

[LoadedAnvils]

Homework Statement

There is a rod falling at a speed v that makes an angle θ with the x-axis as it falls. Is it possible for the intersection point to move faster than light as it falls.

Homework Equations

The Attempt at a Solution

I have done the geometrical calculations and I think yes, it does (which is fine because it's not a particle moving faster than light, only an image) but I am not sure if I am right.

Since it's moving downwards only, the only compression would be vertical and not horizontal so the speed would not decrease. Can anyone tell me if I am correct or not?

 

[haruspex]

I assume the rod is not rotating.
I don't think it even needs to be falling at relativistic speeds, it just needs a very shallow angle. But I'm no expert on relativity, so I may be missing some subtlety.

 

[Doc Al]

Is it possible for the intersection point to move faster than light as it falls.

Sure. No problem.