Length Contraction of spaceships

AI Thread Summary
The discussion revolves around calculating the length contraction of two spaceships moving at relativistic speeds. Spaceship A travels at 0.850c and spaceship B at 0.500c, both initially measuring 1.5 km. The participant initially used a simplified length contraction formula but questioned its adequacy, considering the need for relativistic velocity addition. It was clarified that the relativistic addition of velocities is necessary to accurately determine the length measured by a passenger on one spaceship for the other. The conversation emphasizes the importance of using the correct formulas in relativistic physics.
LeafMuncher
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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?
 
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LeafMuncher said:
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.
 
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!
 
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