Can a beam of light appear to have different trajectories?

[thazard]

Homework Statement

In an inertial reference frame, a beam of light is shone 30 degrees from the x-axis. What is the speed of another inertial reference frame along the x-axis where the beam of light is 90 degrees from the x-axis?

Homework Equations

Can't really think of any equations that would be applicable to this.

The Attempt at a Solution

My reasoning is that this is impossible, which is an option. The speed of light is c in all inertial reference frames, and to the observer in the primed frame, the light would not have its trajectory changed as it is always going at c with respect to them. One of the options is c, which I can understand being the answer as the light would not be moving with respect to the observer in the x-axis, and would have to be in the y-axis. But isn't this impossible - no reference frame can move at c?

 

[mfb]

The speed of light cannot change, but its direction (its velocity) does if you change the reference frame.

This might be easier to see with the opposite direction: Have a beam of light shine orthogonal to the x-axis in reference frame A, now move along the x-axis. Do you expect the light to be still orthogonal to the x-axis? Where would it hit a distant wall in that case, and does that agree with frame A?