How can the observer's speed make events A and B simultaneous?

[satchmo05]

Homework Statement

How fast must the observer be moving in the +x-axis direction so that events A and B occur simultaneously?

Homework 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?

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.

 

[vela]

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.

 

[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.

 

[vela]

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.

 

[satchmo05]

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