As a spaceship moves away from you at half the speed of light, it fires a probe, also away from you at half the speed of light relative to the spaceship. Relative to you, the probe moves at
A)0.80c.
B)0.87c.
C)0.90c.
D)0.95c.
E)c.

Question

Quizplus · Accepted Answer

According to the theory of relativity, velocities don't simply add together. The formula for adding velocities in a relativistic context is $v = \frac{v_1 + v_2}{1 + \frac{v_1 \cdot v_2}{c^2}}$, where $v_1$ and $v_2$ are the velocities of the two objects (in this case, the spaceship and the probe), and $c$ is the speed of light. Plugging in $v_1 = 0.5c$ and $v_2 = 0.5c$, we get $v = \frac{0.5c + 0.5c}{1 + \frac{0.5c \cdot 0.5c}{c^2}} = \frac{1c}{1 + 0.25} = \frac{1c}{1.25} = 0.8c$.

As a Spaceship Moves Away from You at Half the Speed