##### Biographies

# The math behind Michael Jordan’s legendary hang time

Michael Jordan once said, “I don’t know whether I’ll fly or not. I know that when I’m in the air sometimes I feel like I don’t ever have to come down.” But thanks to Isaac Newton, we know that what goes up must eventually come down. In fact, the human limit on a flat surface for hang time, or the time from when your feet leave the ground to when they touch down again, is only about one second, and, yes, that even includes his airness, whose infamous dunk from the free throw line has been calculated at .92 seconds.

And, of course, gravity is what’s making it so hard to stay in the air longer. Earth’s gravity pulls all nearby objects towards the planet’s surface, accelerating them at 9.8 meters per second squared. As soon as you jump, gravity is already pulling you back down. Using what we know about gravity, we can derive a fairly simple equation that models hang time. This equation states that the height of a falling object above a surface is equal to the object’s initial height from the surface plus its initial velocity multiplied by how many seconds it’s been in the air, plus half of the gravitational acceleration multiplied by the square of the number of seconds spent in the air.

Now we can use this equation to model MJ’s free throw dunk. Say MJ starts, as one does, at zero meters off the ground, and jumps with an initial vertical velocity of 4.51 meters per second. Let’s see what happens if we model this equation on a coordinate grid. Since the formula is quadratic, the relationship between height and time spent in the air has the shape of a parabola. So what does it tell us about MJ’s dunk? Well, the parabola’s vertex shows us his maximum height off the ground at 1.038 meters, and the X-intercepts tell us when he took off and when he landed, with the difference being the hang time. It looks like Earth’s gravity makes it pretty hard for even MJ to get some solid hang time.

But what if he were playing an away game somewhere else, somewhere far? Well, the gravitational acceleration on our nearest planetary neighbor, Venus, is 8.87 meters per second squared, pretty similar to Earth’s. If Michael jumped here with the same force as he did back on Earth, he would be able to get more than a meter off the ground, giving him a hang time of a little over one second.

The competition on Jupiter with its gravitational pull of 24.92 meters per second squared would be much less entertaining. Here, Michael wouldn’t even get a half meter off the ground, and would remain airborne a mere .41 seconds. But a game on the moon would be quite spectacular. MJ could take off from behind half court, jumping over six meters high, and his hang time of over five and half seconds, would be long enough for anyone to believe he could fly.