Relative Speed and Size of Two Spaceships Traveling in Opposite Directions

AI Thread Summary
The relative speed of two spaceships traveling in opposite directions, each at 0.8c, is calculated using the relativistic velocity addition formula, resulting in a relative speed of 0.994c. To determine their relative size, the Lorentz factor must be applied, which accounts for time dilation and length contraction effects due to their high speeds. This means that each spaceship will appear contracted in the direction of motion when viewed from the other spaceship's frame of reference. The discussion emphasizes the importance of understanding relativistic effects rather than simply adding their speeds. Proper application of these principles is crucial for solving the problem accurately.
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Homework Statement


Two spaceships are traveling relative to Earth (stationary). One spaceship is going to the right at 0.8c the other is going to the left at 0.8c.

a. What is their relative speed to one another?
b. what is their relative size?

Homework Equations


The Attempt at a Solution

 
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How have you approached the problem so far?
Do you know how to find the Lorentz factor?
 
You have the rest frame of one spaceship S' and the rest frame of the other spaceship S'', one is moving relative to the Earth with velocity 0.8c and one with -0.8c. You know that the two can't be approaching each other at 1.6c! So what do you have to do?
 

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