Special relativity question - Composition of Velocities

Re: Special relativity question - Composition of Velocities

Wait... is this just utilizing length contraction equations? I have a very strong feeling high school physics are not the answer to this lol

Re: Special relativity question - Composition of Velocities

Did some reading, take it with a grain of salt. I'm not too sure if you have to prove this first though:
"So for speeds less than the speed of light, the speed of A relative to B equals the speed pf B relative to A"



EDIT: if the above is true, then finding the length should be pretty simple using the length contraction formula

EDITv2: I haven't taken a single physics course, so I would take anything I say as naive suggestions :P

EDITv3: I'd try to see if you get a more credible source or to prove it yourself. It's not wise to just assume things we often take for granted such as communitivity or particular symmetries.

EDITv4:

I think I've got it:

using the composition of velocities:

the velocity of ship B from A's viewpoint = f(the velocity of A from B's viewpoint, the velocity of B from B's viewpoint) where f is the velocity addition formula (I substituted fly = B, ship = B, shore =A in wikipedia's example: http://en.wikipedia.org/wiki/Velocity-addition_formula).

Now assuming the velocity of B relative to B is zero (if this is not correct, someone please correct me), we have:

the velocity of B from A = f(the velocity of A from B, 0) = (the velocity of A from B + 0) / (1+(the velocity of A from B)(0)/(c^2))) = the velocity of A from B / (1+0) = the velocity of A from B

EDITv5:

because I have no life, spoiler alert:

Re: Special relativity question - Composition of Velocities

yeah the first thing is to realize that if B sees A move at .6c, then A will see B moving at .6c.

from there it's simple length contraction

Re: Special relativity question - Composition of Velocities

Of course, the length contraction equation as well, my bad I forgot to mention it. Haven't read the posts in detail, will do right now. Thanks guys!

Re: Special relativity question - Composition of Velocities

Omfg you're kidding me! It was only that simple! I at once figured the speed of B relative to itself was 0, but then scratched that idea since I thought it induced a division by 0 in the composition of velocities. I must've been really tired while trying this yesterday. Argh!!

Thanks a lot Reuben for the detailed post, that was excellent and will help me greatly!

Re: Special relativity question - Composition of Velocities

No problem (^)> Like I said earlier though, I haven't taken any physics courses so you'll want to double check and verify everything and to take what I say with a grain of salt.