# Relativistic Momentum Help With Equation Reduction

1. Aug 17, 2011

### jimbobian

Hi, so basically have been looking at http://en.wikibooks.org/wiki/Special_Relativity:_Dynamics#Momentum" and working my way through the maths for myself. However I have hit this point and can't get past it:

\begin{align}
u = \frac{v - u}{1-\frac{uv}{c^2}}
\end{align}
Which should be able to become:
\begin{align}
u = \frac{c^2}{v(1-\sqrt{1-\frac{v^2}{c^2}})}
\end{align}
I have tried and tried but can't seem to get it to work. Can anyone help me out on this one please?!

Thanks
James

Last edited by a moderator: Apr 26, 2017
2. Aug 17, 2011

### G01

That wiki entry is not being clear with it's order of operations!

What you should be getting is:

$$u = \frac{c^2}{v}(1-\sqrt{1-\frac{v^2}{c^2}})$$

Last edited by a moderator: Apr 26, 2017
3. Aug 17, 2011

### jimbobian

Hi G01, thanks for your reply. Have tried aiming for that equation instead and still can't get there. I have tried all sorts of different approaches, such as getting it in the form of a quadratic or dividing the top and bottom of the original fraction by c^2, but I just end up nowhere. Could you perhaps give me a hand in the right direction, maybe the first step or two - but don't make it too easy for me!

4. Aug 17, 2011

### Staff: Mentor

Show us exactly what you've tried, and where you get stuck, and tell us why you're stuck.

5. Aug 17, 2011

### jimbobian

Ok, have shut my computer down now and am replying on my phone. I will post my attempts tomorrow.
Thanks,
James

6. Aug 17, 2011

### PAllen

7. Aug 19, 2011

### jimbobian

Haha, went back over my general quadratic attempt after PAllen's suggestion and realised that I had made a rather fundamental cross multiplication error! Fixed that and got to the desired equation. Lovely!

Last question, the equation that I get is:
\begin{align}
u = \frac{c^2}{v}(1\pm\sqrt{1-\frac{v^2}{c^2}})
\end{align}
I assume that we choose the negative version of the equation, because the positive version would yield a value for u which is greater than c?

Cheers