Two spaceships approach Earth from the same direction.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)0.13c
B)0.14c
C)0.15c
D)0.16c
E)0.18c

Question

Quizplus · Accepted Answer

The relative speed between two objects moving in the same direction in special relativity is given by the formula $v_{rel} = \frac{v_2 - v_1}{1 - \frac{v_2v_1}{c^2}}$, where $v_1$ and $v_2$ are the velocities of the two objects (with $v_2 > v_1$) and $c$ is the speed of light. Plugging in $v_1 = 0.21c$ and $v_2 = 0.34c$, the calculation simplifies to $v_{rel} = \frac{0.34c - 0.21c}{1 - (0.34)(0.21)} = \frac{0.13c}{1 - 0.0714} = \frac{0.13c}{0.9286} \approx 0.14c$.

Two Spaceships Approach Earth from the Same Direction