Two spacecraft are traveling toward each other each with a speed of 0.60 c. The speed at which they are approaching each is

Question

Quizplus · Accepted Answer

When two objects are moving towards each other in a relativistic context (i.e., at a significant fraction of the speed of light), their relative speed is not simply the sum of their speeds due to the effects of special relativity. The formula to calculate the relative velocity $v_{rel}$ in such a context is given by $$v_{rel} = \frac{v_1 + v_2}{1 + \frac{v_1 \cdot v_2}{c^2}}$$ where $v_1$ and $v_2$ are the velocities of the two objects (in this case, both 0.60c) and $c$ is the speed of light. Plugging in the values, we get $$v_{rel} = \frac{0.60c + 0.60c}{1 + \frac{(0.60c) \cdot (0.60c)}{c^2}} = \frac{1.2c}{1 + 0.36} = \frac{1.2c}{1.36} \approx 0.88c.$$

Two Spacecraft Are Traveling Toward Each Other Each with a Speed