Two spaceships leave the Earth in opposite directions, each with aspeed of 0.453

Question

Two spaceships leave the Earth in opposite directions, each with aspeed of 0.453c with respect to the Earth. What is thevelocity of spaceship 1 relative to spaceship 2? Take the directionof spaceship 1 to be positive. Express as fraction of c.Do not enter unit.
What is the velocity of spaceship 2 relative tospaceship 1? Express as fraction of c. Do not enterunit.


I used the equation VE2= VE1 +V12/[1+VE2V12/c2]

I can't seem to get the right answer. Do I use 0.453c for V1 and-0.453c for V2 and because I want to look for V of ship 1 relativeto ship 2 must I rearrange the eq.??
What is the velocity of spaceship 2 relative tospaceship 1? Express as fraction of c. Do not enterunit.


I used the equation VE2= VE1 +V12/[1+VE2V12/c2]

I can't seem to get the right answer. Do I use 0.453c for V1 and-0.453c for V2 and because I want to look for V of ship 1 relativeto ship 2 must I rearrange the eq.??

Explanation / Answer

the speed of spaceship 1 relative to earth is v1E =v1 - vE = +0.453c ---------(1) the speed of spaceship 2 relative to earth isv2E = v2 - vE = -0.453c----------(2) the velocity of spaceship 2 relative to spaceship 1 v21 = v2 - v1 ------------(3) subtracting equation (1) from equation (2) we get v2 - v1 = -0.453c - (+0.453c) = -0.453c- 0.453c = -0.906c -----------(4) from equations (3) and (4) we get v21 = -0.906c the negative value of velocity indicates that the twospaceships travel in opposite direction. subtracting equation (1) from equation (2) we get v2 - v1 = -0.453c - (+0.453c) = -0.453c- 0.453c = -0.906c -----------(4) from equations (3) and (4) we get v21 = -0.906c the negative value of velocity indicates that the twospaceships travel in opposite direction.

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