Spacetime Diagrams - Help With Drawing

Lissajoux

1. The problem statement, all variables and given/known data

I need to draw carefully labelled spacetime diagrams (one per section) to illustrate the following:

a) The length of a 'rod' which is exactly [itex]1.0[/itex] light seconds long when at rest along the x′-axis in one frame, and which is moving along the x-axis at [itex]0.866c[/itex] in the diagram rest frame.

b) The addition of velocities as viewed from a spaceship, for the case of a missile launched at [itex]+0.80c[/itex] relative to the spaceship, itself travelling at [itex]+0.60c[/itex] relative to the Earth. Take the launch time to be at [itex]t=0[/itex] as the spaceship passes the Earth.

2. Relevant equations

Within the question statement and solutions, as relevant.

3. The attempt at a solution

I can't figure out how to draw the scenario in (a). No idea. Have managed to do some simpler ones and the one in the second part of this post, but I just can't get my head around how to draw this one.

I've had a go at (b), this is what I have for the spacetime diagram (see the included image) but I'm not sure if the scales and labels are correct, I just made the 3,4,5 values as that was convenient numbers that seem to work from some quick calculations, I think I can just do that.:

http://yfrog.com/5nspacetimediag1j

Any help, particularly with (a) as I think (b) is pretty much correct hopefully, would be much appreciated.