Question

A spaceship moves away from a space station at one-half the speed of light. If a person in the space station flashes a light beacon, people in the ship will see light traveling toward them at a speed of what?

Answer 1

The people in the ship will see light travelling toward them at speed of light.

Explanation:

As the spaceship is moving away from the space station with one half speed of light. The light travelling from the space station with velocity c which is also termed as speed of light will be moving relative to the people in spaceship. So the relative velocities can be found as

                 $u^{\prime}=\frac{u-v}{1-\frac{u v}{c^{2}}}$

In this case, u’ is the speed of light seen by the people in spaceship and u is the velocity of light while v is the velocity of moving spaceship.So u =c and v = $\frac{c}{2}$. Then

                $u^{\prime}=\frac{c-c / 2}{1-\frac{c \times c / 2}{c^{2}}}=\frac{c / 2}{1-\frac{c^{2}}{2 c^{2}}}=\frac{c / 2}{1 / 2}=c$

Thus, the light travelling towards the people in the ship will view that light with the speed of light itself.