Question

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?

Answer 1

Answer question

Answer 2

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