This is the Human Catapult. You can find it on the New River Gorge Bridge in West Virginia on only one day a year: Bridge Day. And as SB Nation details, it's a catapult that throws BASE jumpers off the bridge.
SB Nation wrote this excellent story right here on what the hell Bridge Day is and why there's a catapult there. I can give you the short version.
Back in 1977, West Virginia opened the New River Gorge Bridge, the highest and longest arch span in the Western Hemisphere, as SB Nation points out. In 1980, the first Bridge Day was held to commemorate its opening. How did people make that commemoration? By jumping into the 876 gorge below.
Bridge Day has been running ever since (except for 2001 over terrorism concerns), and it's the only place in the world where people can easily go and watch BASE jumping happen on schedule.
The catapult? Well, that's pretty straightforward. It's a catapult with a seat on it. You get in, pressurized air launches you about 20 feet up and about 50 feet out, and there you are, backflipping off the bridge. Registration is $99. It was first used last year and it was back again for 2013, launching something around 65 people out of something around eight or nine hundred jumpers in that time period.
According to the Bridge Day website, it's quite the experience.
Even the most experienced BASE jumpers with decades of parachuting experience were visibly nervous before being launched over the third tallest bridge in the USA.
There are many other associated costs of Bridge Day (detailed here and here), but there's no getting around the sheer, unbridled American wonder of a catapult that launches you off a giant bridge, so long as you have a parachute and know how to use it.
Video Credits: iLoveSkydiving.org