Question

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?

Answer 1

The velocity of the ions relative to the earth observer is
`v = 0.63 c`

Step-by-step explanation:

From the question we are told that

The speed of the alien ship is
`v_a = 0.3c`

The speed of the iron gun is
`v_g = 0.4c`

The motion of the ions relative to the earths observer can be mathematically represented as

`v = (v_a + v_g)/([(1+ v_av_g)/(c^2) ])`

substituting values

`v = ( 0.3c + 0.4c)/([(1+ 0.3c * 0.4c)/(c^2) ])`

=>
`v = 0.63 c`