Solving for Simultaneity problem

1. Aug 28, 2010

satchmo05

1. The problem statement, all variables and given/known data
How fast must the observer be moving in the +x-axis direction so that events A and B occur simultaneously?

2. Relevant equations
I am currently in the solving stage of this problem and I need some help factoring this out/entering it into Octave. Can anyone help?

3. The attempt at a solution
I am currently nearing the end of the (*hopefully) working solution. I am currently here:

1.296e33=v^2(9e16-v^2)

How do I solve from here either by hand, or by entering it into MATLAB/Octave? I appreciate all help! Thank you very much for your time.

2. Aug 29, 2010

vela

Staff Emeritus
In relativity, it's generally better to solve for β=v/c rather than v alone. It just keeps things neater. In your case, if you divide by c4, you'll get

$$\beta^2(1-\beta^2) = 0.16$$

This is a quadratic in β2. Solve for β2 by factoring, if possible, or by using the quadratic equation.

3. Aug 29, 2010

satchmo05

Thank you for your reply. However, by entering that function into my calculator, I find that the function has 4 zeros. Even if I assume that the velocity cannot be negative (because we're moving in the +x direction), I still have two values that are directly proportional by a factor of 2. How do I determine which one it is? The values end up being 0.447214c and 0.89443c FYI. Thanks.

4. Aug 29, 2010

vela

Staff Emeritus
I can't say as I don't know how you got that equation. I'm guessing to get to that point you squared another equation, which introduced a spurious solution. If that's the case, you just have to try both solutions in the original equation and see which one works.

5. Aug 29, 2010

satchmo05

I found the zeros to the equation you gave me above...