Two spacecraft are moving relative to the Earth at a speed of 0.75s in opposite directions. What is their relative speed from the point of view of each of the astronauts?
Data: Vк1 – the speed of the first cosm. ship (Vк1 = 0.75 С); Vк2 is the speed of the second cosm. ship (Vк1 = 0.75 С); Vk = Vk1 = Vk2.
Const: C – the speed of light (for the calculation prin. C ≈ 3 * 10 ^ 8 m / s).
To find out the relative speed of space. spacecraft from the point of view of astronauts, we apply the relativistic z-n of addition of velocities: Vx = (Vk1 + Vk2) / (1 + Vk1 * Vk2 / C ^ 2) = 2Vk / (1 + Vk ^ 2 / C ^ 2) = 2Vk / (1 + (Vk / C) ^ 2).
Let’s perform the calculation: Vx = 2Vk / (1 + (Vk / C) ^ 2) = 2 * 0.75C / (1 + (0.75C / C) 2) = 1.5C / (1+ 0.75 ^ 2 ) = 1.5C / 1.5625 = 0.96C = 2.88 * 10 ^ 8 m / s.
Answer: The relative speed of space. ships is 0.96C or 2.88 * 10 ^ 8 m / s.
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