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

Answer:

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

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

       $v = \frac{v_a + v_g}{[\frac{1+ v_av_g}{c^2} ]}$

substituting values

     $v = \frac{ 0.3c + 0.4c}{[\frac{1+ 0.3c * 0.4c}{c^2} ]}$

 =>   $v = 0.63 c$