A spaceship is moving in a straight line away from Earth at 0.80c, measured relative to Earth. It launches a missile that moves away from the spaceship in the forward direction at 0.60c, relative to
The ship. Relative to Earth, what is the speed of this missile?
A) c
B) greater than 0.80c but less than c
C) greater than c but less than 1.4c
D) 1.4 c

Question

Quizplus · Accepted Answer

To find the speed of the missile relative to Earth, we use the formula for addition of velocities in special relativity: $v = \frac{v_1 + v_2}{1 + \frac{v_1v_2}{c^2}}$, where $v_1 = 0.80c$ is the speed of the spaceship relative to Earth, $v_2 = 0.60c$ is the speed of the missile relative to the spaceship, and $c$ is the speed of light. Plugging in these values, we find that the speed of the missile relative to Earth is greater than 0.80c but less than c, making option B correct.

A Spaceship Is Moving in a Straight Line Away from Earth