# Relativistic time, distance and velocity

As you wish....
I prefer to draw pictures and to reason geometrically and invariantly...
rather than do algebra where [without at least a clear picture]
one is likely to be merely pushing around some symbols [which, as you see, can easily lead to mixups].

For this problem, I didn't have to deal with any complicated expressions for v.... it sort of just fell out... especially if you can reason trigonometrically.

Lots of things are simple... assuming you set them up correctly.

My \$0.02.

EDIT:
As you pointed out earlier... this is a GRE question.
Some will take the long "time consuming" road... involving possibly "messy equations"...
others will avoid the "messy equations" and see that it is really "somewhat simple".

I actually never learned to used spactime diagrams in the manner that you displayed. If I did, I don't remember. My last modern physics course with relativity was in the late '80s, or maybe 1990.

And the book I've been using to study for the GRE also didn't cover them. It only covered the Lorentz transforms.

While I appreciate robphy's approach of using spacetime diagrams, solving this sort of problem is a breeze if you understand the relativistic behavior of clocks and metersticks. (I do strongly agree that the best way to deepen your understanding of special relativity is to learn how to use spacetime diagrams.) Just plugging into the Lorentz transformations without a clear picture to guide you can often lead to nonsense.

I agree. I'm going to have to sit down sometime and learn them.

I've been out of college for about 14 years and my degree is MS in EE, not physics. But I've been reviewing fundamentals of physics because I have applied to physics PhD programs at three universities.