A spaceship approaching an asteroid at a speed of 0.60c launches a scout rocket with speed 0.40c relative to the spaceship.At what speed is the scout rocket approaching the asteroid?
A)0.81c
B)1.0c
C)0.76c
D)0.64c
E)0.96c

Question

Quizplus · Accepted Answer

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

A Spaceship Approaching an Asteroid at a Speed of 0