# GPS hyperbola question

• Jul 16th 2013, 09:15 PM
minneola24
GPS hyperbola question
A bit of a crazy question and in completely lost.

I fully understand how to graph hyperbolas but how do I deal with the .001 second variable?

ThanksAttachment 28842
• Jul 16th 2013, 09:47 PM
earboth
Re: GPS hyperbola question
Quote:

Originally Posted by minneola24
A bit of a crazy question and in completely lost.

I fully understand how to graph hyperbolas but how do I deal with the .001 second variable?

ThanksAttachment 28842

1. A time difference of 0.001 s correspond to a distance of 186 miles.

2. To determine the x-coordinate of the ship's position use the definition of the hyperbola as the locus of points whose difference of the distances to two fixed points is a constant. You have to solve for x:

$\sqrt{(-150-x)^2+75^2} - \sqrt{(150-x)^2+75^2} =186$

3. For confirmation only: I've got $x \approx 110.3$