Spaceships A and B are moving in the same direction. Spaceship A is moving at 0.80 c relative to a stationary observer, and spaceship B is moving at 0.80 c relative to spaceship A. What does the stationary observer find for the speed of spaceship B?
A) 1.6 c
B) 1.3 c
C) 1.0 c
D) 0.78 c
E) 0.98 c

Question

Quizplus · Accepted Answer

To find the relative speed of spaceship B as observed by the stationary observer, we use the formula for relativistic addition of velocities: $v = \frac{v_1 + v_2}{1 + \frac{v_1 \cdot v_2}{c^2}}$, where $v_1 = 0.80c$ (speed of A relative to the observer), $v_2 = 0.80c$ (speed of B relative to A), and $c$ is the speed of light. Plugging in the values, we get $v = \frac{0.80c + 0.80c}{1 + \frac{0.80c \cdot 0.80c}{c^2}} = \frac{1.6c}{1 + 0.64} = \frac{1.6c}{1.64} \approx 0.98c$. This shows that due to the effects of special relativity, speeds don't simply add up linearly when approaching the speed of light.

Spaceships a and B Are Moving in the Same Direction