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Spaceships A and B are both moving at the speed 0.9c relative to Earth, but in...

Spaceships A and B are both moving at the speed 0.9c relative to Earth, but in opposite directions. a) Find the speed of spaceship A relative to spaceship B. b) find the gamma factor γ for the motion of A relative to B. c) Johnny, in spaceship A, measures the speed of a light pulse along the direction of the motion to be c. Use the same formula you used for part a) (ux’ as a function of ux) to find the speed of the pulse measured by the observer on spaceship B.

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Answer #1

The relative velocity of any two objects never exceeds the velocity of light. According to Einstein velocity addition relationships, you can write

Here, uBA is the relative speed of B with respect to A. Here, A and B are moving towards each other with speed uA and uB respectively. In your problem, two objects are moving in the opposite direction and hence one speed will be negative in the expression above.

(a) The relative speed of A relative to spaceship B will be

(b)  the gamma factor γ for the motion of A relative to B will be

(c) In spaceship A, the speed of a light pulse along the direction of the motion will be

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