Lorentz velocity transformations - relativity

[tatiana_eggs]

Homework Statement

Two spaceships approach each other, each moving with
the same speed as measured by an observer on the
Earth. If their relative speed is 0.70c, what is the speed of
each spaceship?

My current understanding of the problem.
S= wrt observer on Earth
S'=wrt one of the spaceships
u= ??
u'=speed of spaceship B if S' is wrt spaceship A.
v = speed of S' wrt S (how does v fit into this problem?)

Homework Equations

I'm great with the equations and algebra of Lorentz transformations, I'm just having trouble understanding/visualizing what the question is asking and assigning variables to knowns and unknowns.

u' = u-v / (1-uv/c²)

The Attempt at a Solution

I'd appreciate it if someone could reword the problem or answer me:

What does "their relative speed" mean? Is that their speed in S (wrt Earth) or relative to each other? Also, when "what is the speed of each spaceship" is asked, do they mean the speed of each spaceship relative to Earth or relative to each other? Lastly, are "with respect to" and "relative to" interchangeable terms?

Thanks a bunch

 

[Maxim Zh]

The relative speed usually means the speed of an object in the coordinate system bound to the other object. The task would be too simple oterwise.

So we already know the speed of each spaceship relative to the other (it's 0.70c) and you should derive their speed in S.

 

[Altabeh]

Homework Statement

Two spaceships approach each other, each moving with
the same speed as measured by an observer on the
Earth. If their relative speed is 0.70c, what is the speed of
each spaceship?

My current understanding of the problem.
S= wrt observer on Earth
S'=wrt one of the spaceships
u= ??
u'=speed of spaceship B if S' is wrt spaceship A.
v = speed of S' wrt S (how does v fit into this problem?)

Homework Equations

I'm great with the equations and algebra of Lorentz transformations, I'm just having trouble understanding/visualizing what the question is asking and assigning variables to knowns and unknowns.

u' = u-v / (1-uv/c²)

The Attempt at a Solution

I'd appreciate it if someone could reword the problem or answer me:

What does "their relative speed" mean? Is that their speed in S (wrt Earth) or relative to each other? Also, when "what is the speed of each spaceship" is asked, do they mean the speed of each spaceship relative to Earth or relative to each other? Lastly, are "with respect to" and "relative to" interchangeable terms?

Thanks a bunch

1- Let A and B be our spaceships. The "relative speed" here is the speed of spaceship B measured by an onboard observer in A's frame and vice versa.

2- The relative speed is meant to be the one belonging to B, for example, that an onboard observer on A measures in the frame of his own.

3- Here the "speed" of each spaceship refers to the speed measured with respect to an observer being at rest on the Earth.

4- In the textbooks around the topic of GR or SR, authors mostly prefer to use 'relative to' in place of with 'respect to'. But if you saw the latter somewhere, you wouldn't be panicking yourself as it is the same as 'relative to'.

But about the main question: Just make use of Maxim's idea.

AB

 

[tatiana_eggs]

Thanks so much, guys, that really helped me. I got the answer now.