Last week I ran a half marathon. I know, foolish. But the main reason I did it is because it was in San Francisco and the course crossed the Golden Gate Bridge twice. You can see the bridge from a distance in downtown San Francisco. You can also see it driving across in a car, but it goes by pretty quick. Neither of those are the same experience as crossing it on foot. The cable droops down almost all the way to the road. It was fun to get right up close to it. Its just about head level at its lowest point.
An interesting thing I noticed is that the roadway is curved. You definitely run a bit uphill then down. The highest point, though, is not in the middle. I'm sure engineers had a reason for that, but that would be beyond me.
You can get many statistics regarding the bridge on-line. I was going to cut and paste them here, but they are easy to find. A teacher could fashion math applications for anything from arithmetic to calculus. A cool one is to find the equation of a parabola approximating the cable.
Since the cable is about head-height, using the roadway as the x-axis, we can take the center of the cable to be the point (0,6). The distance between the two towers is 4,200 feet. The height of the towers above the roadway is 500 feet. So, two other points on the cable could then be (2,100, 500) and (-2,100, 500). Using a system of equations with those three points could give you an equation of a parabola.
Also, the distance from the mean high water mark to the road is 220 feet. So a parabola could be found with the Pacific Ocean represented by the x-axis.
Or it could be found using meters rather than feet.
You could probably spend a week just studying the bridge. And it would make for a cool field trip.
