A spacecraft approaching the earth launches an exploration vehicle. After the launch, an observer on earth sees the spacecraft approaching at a speed of 0.35c and the exploration vehicle approaching at a speed of 0.80c. What is the speed of the exploration vehicle relative to the spaceship?
If an observer (like the one on the earth) observes two objects
moving with respect to the observer with speeds u and v, the
relativistic addition of velocities can be used to determine the
speed of the two objects with respect to each other
the relativistic addition of velocities becomes:
(u-v)/(1-(uv/c^2))
the numerator is the Galilean relative velocity
here, u=0.8c and v=0.35c, so we have
relative velocity of exploration vehicle to spaceship =
(0.8c-0.35c)/[1-(0.8c)(0.35c)/c^2] =
(0.45c)/(1-0.28C^2/c^2) = 0.45c/0.72 =0.625c
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