Spaceship A travels at 0.400c relative to an earth observer. According to the sa

Question

Spaceship A travels at 0.400c relative to an earth observer. According to the same observer, spaceship A overtakes a slower moving spaceship B that moves in the same direction. The captain of B sees A pass her ship at 0.114c. Determine the speed of B relative to the earth observer.

I know that I have to use one of the below equations. But I have no idea what the thought process is in deciding which one to use. I also do not know which variable to assign to which velocity. Can you please explain the answer and in addition how to solve these type of problems in general (i.e. which equation to use when as well as which variable to assign to which velocity).

Thank you so much!

Explanation / Answer

Both equations are the exact same, just rearranged, so it does not matter which one you use, its just easier sometimes if you need u to use the first one, if you need u', use the second one.

However, in this case, we need to solve for v, so we will need to rearrange again to find v

u = the velocity of an obect (the spaceship) relative to ans observer u = .400c

u' = the same object as seen from the different frame (seen from B) u' = .114c

v = the velocity of the other frame (frame B, which we are asked to find)

Rearranging the equation gives us...

v = u' - u/(uv'/c2 -1)

v = (.114c - .400c)/[(.114)(.400) - 1]

v = .300 c

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