Two spaceships leave Earth in opposite directions, each with a speed of 0.58c with respect to Earth.

Two spaceships leave Earth in opposite directions, each with a speed of 0.58c with respect to Earth. What are the velocities of spaceship 1 relative to spaceship 2 and spaceship 2 relative to spaceship 1?

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    Since both the spaceships are moving in opposite direction, consider \[ V_B = \text{Velocity of spaceship 2} = 0.58c \] \[ V_A = \text{Velocity of spaceship 1} = -0.58c \] \[ V_{B/A} = \frac{V_B – V_A}{1 – \frac{V_B \cdot V_A}{c^2}} \] \[ \Rightarrow V_{B/A} = \frac{0.58c – (-0.58c)}{1 – \frac{0.58c (-0.58c)}{c^2}} \] \[ \Rightarrow V_{B/A} = 0.868c \]Similarly, \[ V_{A/B} = \frac{V_A – V_B}{1 – \frac{V_A \cdot V_B}{c^2}} \] \[ \Rightarrow V_{A/B} = \frac{-0.58c – 0.58c}{1 – \frac{-0.58c(0.58c)}{c^2}} \] \[ \Rightarrow V_{A/B} = -0.868c \]Velocity of aircrafts relative to each other is 0.868c.

    techAir Answered 4 days ago.
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