How Do You Calculate Relative Speed in Special Relativity?

[Jalo]

Homework Statement

Two spaceships (A and B) are traveling in opposite ways. An observer in Earth measures both velocities.
The speed of ship A (Va) = 0.75c.
The speed of ship B (Vb) = 0.85c.
What's the speed of **** B regarding ship A?

Homework Equations

The Attempt at a Solution

At first I tried solving it using Galileu's relativity, but I've reached the result of 1.6c.
Then I remembered that when we're dealing with speeds close to c we have to use Einstein's special relativity, so I've looked around all the formulas I have but none of them involved velocity, only time, spaceship length, and there are also the ones involving energy but I don't think that has nothing to do with this exercise.

Thanks!

 

[Doc Al]

Read: Einstein Velocity Addition

 

[Jalo]

Read: Einstein Velocity Addition

I've used u'= -.85c and v=.75c

Substituting I got u= -.85c-.75c / 1-(-.85*.75) = -.977c

Therefore the speed of ship B regarding ship A is -0.977c

Is that solution correct? I think I've done everything right but i'd like to be sure :D

Thanks!

 

[Doc Al]

Good. The relative speed is correct, which is all you need. (The sign depends on your convention.)