Length contraction of two spaceships

[Saxby]

Homework Statement

Two space ships, each a hundred metres long when measured at rest, travel toward each other with a speed of 0.85c relative to the Earth.

Homework Equations

λ = 1 / √1 - (v²/c²)
x' = λ(x - vt)
L' = L / λ

The Attempt at a Solution

Well to be honest i may be missing an equation or something but that's what i was given.

I find that the relative velocity of one spaceship to another (according to Newton) would be 1.5c. This doesn't work using the equations above. I know i have to find the relative velocity according to Einstein's theory but i don't know how.

 

[Mandelbroth]

Homework Statement

Two space ships, each a hundred metres long when measured at rest, travel toward each other with a speed of 0.85c relative to the Earth.

Homework Equations

λ = 1 / √1 - (v²/c²)
x' = λ(x - vt)
L' = L / λ

The Attempt at a Solution

Well to be honest i may be missing an equation or something but that's what i was given.

I find that the relative velocity of one spaceship to another (according to Newton) would be 1.5c. This doesn't work using the equations above. I know i have to find the relative velocity according to Einstein's theory but i don't know how.

So, you are trying to find the relative velocity of one to the other?

Let the first spaceship be spaceship A and the second be spaceship B.

Consider $v_{BA}=\frac{v_B-v_A}{1-\frac{v_Av_B}{c^2}}$.