Length Contraction of spaceships

[LeafMuncher]

Homework Statement

Two identical spaceships are under construction. The constructed length of each spaceship is 1.5 km. After being launched, spaceship A moves away from Earth at a constant velocity (speed is 0.850c) with respect to the earth. Spaceship B follows in the same direction at a different constant velocity (speed is 0.500c) with respect to the earth. Determine the length that a passenger on one spaceship measures for the other spaceship.

Homework Equations

L = Lo (1-v^2/c^2)

The Attempt at a Solution

I have:
v = v1 - v2 = 0.850c - 0.500c = 0.350c

L = Lo (1- v^2/c^2) = 1.5km (1 - 0.350^2) = 1.31km

Hi, my question is more whether I'm under-thinking this problem. This solution seems too simple. Should I be using the velocity addition formula or is that only for a third reference frame?

 

[kuruman]

Hi, my question is more whether I'm under-thinking this problem. This solution seems too simple. Should I be using the velocity addition formula or is that only for a third reference frame?

Yes, you should use relativistic addition of velocities. You have three reference frames, two spaceships and the Earth.

 

[LeafMuncher]

Thanks, I was just a bit confused since the sample paper said all relevant formulas would be included, but had no trace of the addition of velocities formula, so I was hesitant to use a formula that wasn't given. Thanks again!