Bungee jumping has been around for ages. The land divers of Vanuatu tied vines around their ankles. The first modern-style jump with elastic cords was undertaken in Bristol, England, in 1979 by the Oxford University Dangerous Sports Club. The idea, of course, is that—if all goes well—the cord stretches and exerts an upward force to keep you from hitting the ground.
But how’s this for a new way to tempt fate: What if you replaced the elastic cord with two magnets? You could put a magnet on the jumper with another magnet on the ground, aligned in such a way that their poles repel. As the person gets close to the ground, magnetic levitation would hopefully buoy them back up. Bungee jumping without a bungee!
That’s the premise behind this video of the supposed “first wireless bungee jump.” Let me be real clear: It’s a fake. It’s really an Ikea commercial. Do NOT try this at home. Don’t even think about trying it.
OK, but … could the concept actually work? We could use trial and error to find out. I suggest we analyze the physics instead. Ready? Let’s jump in.
The Physics of Bungee Jumping
First we need to be clear on why it’s bad to hit the ground. So, here’s the deal. It’s all about acceleration. Suppose a person foolishly jumps off a 10-meter-high ledge. As they fall, the gravitational force pulls down to cause an increase in velocity. Ignoring the air resistance force, this would produce an acceleration of 9.8 m/s2.
Starting from rest, this would put their speed at 14 meters per second just before impact. Now let’s say the jumper stops on the ground over a distance of 5 centimeters. (It’s probably much less than that.) This would produce a stopping acceleration of about 1,960 m/s2. That is 200 g’s. That’s the problem. A human can survive an acceleration of only around 30 to 40 g’s.
So how does the bungee fix the acceleration problem? As the cord stretches, it exerts an upward force on the jumper in the same direction that the ground would push. However, it pushes over a much larger distance, so it produces a much lower acceleration.
Here is a quick numerical model for a bungee jumper starting 10 meters high and just barely touching the ground. (Follow the link to see the animation.) I made the bungee 5 meters long, so it doesn’t start stretching until after that. This gives the following acceleration curve:
