Question

relative to the Earth, spaceship A moves in one direction with speed 0.8c and another spaceship, B, moves in the opposite direction with speed 0.6c. What is the speed of spaceship A as measured by B?

Answer 1

$\text{For an observer on Earth:}$

$v_{EA} = 0.8c$

$v_{EB}= -0.6c$

$\text{For the observer on the B ship: }$

$v_{BE}= 0.6c$

$\text{according to the Lorentz velocity addition:}$

$v_{BA}= \frac{v_{EA}+v_{BE}}{1+\frac{v_{BE}}{c^2}v_{EA}};$

$v_{BA}= \frac{0.8c+0.6c}{1+\frac{0.6c}{c^2}0.8c}=\frac{1.4c}{1.48}\approx0.95c$

$\text{Answer: }v_{BA}\approx0.95c$