Two spaceships approach Earth from opposite directions. One has a speed of 0.21c and the other a speed of 0.34c, both relative to Earth. What is the speed of one spaceship relative to the other?
A) 0.58c
B) 0.55c
C) 0.64c
D) 0.61c
E) 0.51c

Question

Quizplus · Accepted Answer

To find the relative speed of one spaceship to the other, we use the formula for relativistic addition of velocities: $v = \frac{v_1 + v_2}{1 + \frac{v_1v_2}{c^2}}$, where $v_1 = 0.21c$, $v_2 = 0.34c$, and $c$ is the speed of light. Plugging these values in, we get $v = \frac{0.21c + 0.34c}{1 + \frac{(0.21)(0.34)}{1}} = \frac{0.55c}{1 + 0.0714} = \frac{0.55c}{1.0714} \approx 0.51c$.

Two Spaceships Approach Earth from Opposite Directions