Special relativity question - Composition of Velocities

[MarioNintendo]

Hey y'all. I'm back again with a physics question. Been a while since I've done special relativity, and I can't wrap my head around this peculiar problem. Let's see if anyone out there has an idea:



Spaceship B sees A move at 0.6c. A sees B as 400m long.

What is the proper length of B?
What is the velocity of B in the referential of A?

I know we must use the composition of velocities, and of course the Lorentz factor, but that's about it. I'm sure the answer is dumb, but I somehow can't find it. Help? (below is the composition of velocities)

[Spenner]

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

[reuben_tate]

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"

http://physics.stackexchange.com/que...ative-to-light

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:

So for the question: "What is the velocity of B in the referential of A?", by the above, we have that this velocity must also be 0.6c.

Now, for the question, "What is the proper length of B?"

We use the length contraction equation:
L = L_0 * sqrt(1-v^2 / c^2), where
L_0 is the proper length (the length of the object in its rest frame) (the proper length of B)
L is the length observed by an observer in relative motion with respect to the object (length of B as viewed by A)
v is the relative velocity between the observer and the moving object (speed of A relative to B or speed of B relative to A, doesn't matter which we we interpret since we said these were the same earlier)
c is the speed of light (yup)

plugging in what we know:
400m = L_0 * sqrt(1-(0.6c)^2/c^2) = L_0*sqrt(1-0.36) = L_0*sqrt(0.64) = L_0*(4/5)
L_0 = 400m/(4/5) = 500m

[FoJaR]

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

[MarioNintendo]

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!

[MarioNintendo]

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!

[reuben_tate]

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.