Velocity addition: A spaceship approaching an asteroid at a speed of 0.60c launches a rocket forward with a speed of 0.40c relative to the spaceship. At what speed is the rocket approaching the asteroid as measured by an astronaut on the asteroid?

Question

Quizplus · Accepted Answer

The speed of the rocket relative to the asteroid can be calculated using the formula for relativistic velocity addition: $v = \frac{v_1 + v_2}{1 + \frac{v_1v_2}{c^2}}$, where $v_1 = 0.60c$ and $v_2 = 0.40c$. Plugging these values in, we get $v = \frac{0.60c + 0.40c}{1 + \frac{(0.60c)(0.40c)}{c^2}} = \frac{1.0c}{1 + 0.24} = \frac{1.0c}{1.24} = 0.81c$.

Velocity Addition: a Spaceship Approaching an Asteroid at a Speed