Spacecraft A is traveling at a speed of 0.80 c relative to Earth. Spacecraft B is traveling in the same direction as spacecraft A but at a speed of 0.40 c relative to spacecraft A. The speed of spacecraft B relative to Earth is

Question

Quizplus · Accepted Answer

To find the relative speed of spacecraft B with respect to Earth when both spacecraft are moving in the same direction, 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 spacecraft A relative to Earth, $v_2 = 0.40c$ is the speed of spacecraft B relative to spacecraft A, and $c$ is the speed of light. Plugging these values into the formula gives a result of approximately $0.91c$, making option D correct.

Spacecraft a Is Traveling at a Speed of 0