Question

Two spaceships approach each other, each moving with the same speed as measured by a
stationary observer on the Earth. Their relative speed is 0.8c. Determine the velocities of
each spaceship as measured by the stationary observer on Earth.

Answer 1

Answer on question # 51437, Physics, Solid State Physics

Question Two spaceships approach each other, each moving with the same speed as measured by a stationary observer on the Earth. Their relative speed is 0.8c. Determine the velocities of each spaceship as measured by the stationary observer on Earth.

Solution In relativity, velocity-adding formula is

$s=\frac{v+u}{1+(vu/c^{2})}$

where $s$ is relative velocity of two objects, that have velocities $u$ and $v$ in the laboratory (Earth) frame. We know that $u=v$ and $s=0.8c$. So we can find $u=v$:

$0.8c=\frac{2v}{1+v^{2}/c^{2}}$

$2v=0.8c+0.8v^{2}/c$

There is only one solution that is smaller than c, its

$v=0.5c$

So this is velocity measured from Earth.

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