Perception of faster than light travel?

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SUMMARY

The discussion centers on a problem involving the relative velocities of three spaceships (A, B, and C) as observed by the commander of ship B. The commander observes ship C approaching at 0.83c and ship A at 0.48c. The initial attempt to calculate the speed of ship A relative to ship C using the relativistic velocity addition formula yielded an incorrect result of 0.94c, while the correct answer is 1.3c. The key takeaway is that the commander can simply add the velocities in this specific frame without violating the principles of Special Relativity (SR).

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  • Basic knowledge of frame of reference in physics
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metal_maniac
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I'm currently taking a modern physics course, I came across this problem which really threw me off guard:

Three spaceships A, B, and C are in motion as shown in the figure. The commander on ship B observes ship C approaching with a relative velocity of 0.83c. The commander also observes ship A, advancing in the rear, with a relative velocity of 0.48c. As measured by commander on ship B, at what speed is ship A approaching ship C?

Attempt at a solution: I used the transformations equations which resulted in a value of 0.94c.
observed velocity = [(-0.83c) - 0.48c]/[1-(0.83c*0.48c/c^2)] = 0.937c
0.94c was one of the possible answers so I picked it... it was wrong.
The correct answer was 1.3c.

Is this even possible?
I do suppose that someone with no knowledge in physics would just add the two velocities like it was Galilean transformations, but we're taking about the commander of a ship, pretty sure he wouldn't just add them together.
Is this just a badly written question or am I missing some things in my understanding? Any help is appreciated!
Thank you
 
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The relativistic formula for addition of velocities is used when you want to change frames.
Here things are different. You're actually calculating the closing speed of spaceships A and C in the B's frame. He sees A to travel at 0.48c and C to travel at 0.83c, so if he attempts to find the time derivative of the distance between the two, he has no way other than simply adding their velocities.
I should say that this doesn't violate SR since there is no mass or energy going faster than light!
Take a look at here for more information!
 
Last edited:
You're a life saver!
I was stuck on this question for so long, and my textbook had no explanation for it.
Thank you so much!
 

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