Question

spacecraft approaching the earth launches an exploration vehicle. after the launch, an observer on earth sees the spacecraft approaching at a speed of 0.50c and the exploration vehicle approaching at a speed of 0.70c. what is the speed of the exploration vehicle relative to the spaceship?

Answer 1

The speed of the exploration vehicle relative to the spaceship is 0.89 times the speed of light (0.89c).

Step-by-step explanation:

To find the speed of the exploration vehicle relative to the spaceship, we can use the relativistic velocity addition formula. According to this formula, the relative velocity (v') between two objects moving at velocities v1 and v2 is given by:

v' = (v1 + v2)/(1 + (v1*v2)/c^2)

Where c is the speed of light.

In this case, the spacecraft is approaching at a speed of 0.50c and the exploration vehicle is approaching at a speed of 0.70c relative to Earth. Let's substitute these values into the formula:

v' = (0.50c + 0.70c)/(1 + (0.50c*0.70c)/c^2)

= 1.20c/(1 + 0.35)

= 1.20c/1.35

= 0.89c

Therefore, the speed of the exploration vehicle relative to the spaceship is 0.89 times the speed of light (0.89c).