A spaceship is moving away from an asteroid with a speed of 0.80c relative to the asteroid. The spaceship then fires a missile with a speed of 0.50c relative to the spaceship. What is the speed of
The missile measured by astronauts on the asteroid if the missile is fired away from the asteroid?
A) 0.50c
B) 0.65c
C) 0.93c
D) 0.30c
E) 1.3c

Question

Quizplus · Accepted Answer

To find the speed of the missile relative to the asteroid, we use the formula for relativistic velocity addition: $v = \frac{v_1 + v_2}{1 + \frac{v_1v_2}{c^2}}$, where $v_1 = 0.80c$ (speed of the spaceship relative to the asteroid), $v_2 = 0.50c$ (speed of the missile relative to the spaceship), and $c$ is the speed of light. Plugging in these values, we get $v = \frac{0.80c + 0.50c}{1 + \frac{(0.80c)(0.50c)}{c^2}} = \frac{1.30c}{1 + 0.40} = \frac{1.30c}{1.40} = 0.93c$.

A Spaceship Is Moving Away from an Asteroid with a Speed