# Special relativity where am I going wrong?

1. Apr 20, 2017

### Kara386

1. The problem statement, all variables and given/known data
A spaceship moves away from earth at 0.9c and fires a probe in the same direction as its motion at 0.7c. What is the probe's velocity relative to Earth?

2. Relevant equations

3. The attempt at a solution
The Lorentz velocity transformation is $v_x' = \frac{v_x - u}{1-\frac{uv}{c^2}}$, and since in this case we want to find $v_x$ this can be rearranged to get
$v_x = v_x' \left(1-\frac{uv_x}{c^2}\right) + u$
So then if I substitute in numbers, I use $v_x' = 0.7c$ and $u=0.9c$, which gives me an answer greater than the speed of light, so that's wrong.

This is a worked example in a textbook and they've also used $v_x'=0.7c$ and $u=0.9c$ so I have no idea why that isn't working. They're using a different form of the equation, all one fraction and plus on the denominator, not $-\frac{uv_x}{c^2}$. But then shouldn't rearranging the way I have work as well?

The actual answer should be 0.982c. Where am I going wrong??? Did I rearrange wrong?

2. Apr 20, 2017

### Kara386

Yes I did rearrange wrong. Missed the fact that the thing in the brackets isn't $v_x'$ so I haven't actually made $v_x$ the subject. Stupid mistake, sorry. It took me typing it up to spot that!