An earth observer sees an alien ship pass overhead at 0.3c. The ion gun of the alien ship shoots ions straight ahead of the ship at a speed 0.4c relative to the ship. What is the speed of the ions relative to the earth observer?

Question

Quizplus · Accepted Answer

To find the speed of the ions relative to the earth observer, we use the relativistic velocity addition formula: $ v = \frac{u + v'}{1 + \frac{uv'}{c^2}} $, where $ u = 0.3c $ (speed of the ship relative to Earth) and $ v' = 0.4c $ (speed of ions relative to the ship). Plugging in these values, we get $ v = \frac{0.3c + 0.4c}{1 + \frac{0.3c \cdot 0.4c}{c^2}} = \frac{0.7c}{1 + 0.12} = \frac{0.7c}{1.12} \approx 0.63c $.

An Earth Observer Sees an Alien Ship Pass Overhead at 0.3c