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)0.30c
B)0.50c
C)0.93c
D)1.3c
E)0.65c

Question

Quizplus · Accepted Answer

Using the relativistic velocity addition formula:
v = (u + v)/(1 + uv/c^2)
where u=0.50c, v=0.80c, and c is the speed of light
v = (0.50c + 0.80c)/(1 + (0.50c)(0.80c)/c^2) = 1.3c/(1 + 0.4) = 0.93c
Therefore, the speed of the missile measured by astronauts on the asteroid is 0.93c.

A Spaceship Is Moving Away from an Asteroid with a Speed