By | February 23, 2017

## The math behind Michael Jordans legendary hang time Andy Peterson and Zack Patterson

Michael Jordan once said, quot;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 everhave to come down.quot; But thanks to Isaac Newton, we know that what goes upmust eventually come down. In fact, the human limit on a flat surface for hang time, or the time from when your feet leavethe 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 itso hard to stay in the air longer. Earth's gravity pulls all nearby objectstowards 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 equationthat models hang time. This equation states that the heightof a falling object above a surface is equal to the object's initial heightfrom the surface plus its initial velocity multiplied by how many secondsit's been in the air, plus half of the gravitational acceleration multiplied by the square of the numberof seconds spent in the air. Now we can use this equation to modelMJ's free throw dunk.

Say MJ starts, as one does,at zero meters off the ground, and jumps with an initial verticalvelocity of 4.51 meters per second. Let's see what happens if we modelthis equation on a coordinate grid. Since the formula is quadratic, the relationship between heightand time spent in the air has the shape of a parabola. So what does it tell us about MJ's dunké Well, the parabola's vertex shows ushis maximum height off the ground

at 1.038 meters, and the Xintercepts tell us when he took off and when he landed,with the difference being the hang time. It looks like Earth's gravitymakes it pretty hard for even MJ to get some solid hang time. But what if he were playing an away gamesomewhere else, somewhere faré Well, the gravitational accelerationon our nearest planetary neighbor, Venus, is 8.87 meters per second squared, pretty similar to Earth's.

If Michael jumped here with the sameforce 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 Jupiterwith its gravitational pull of 24.92 meters per second squaredwould be much less entertaining. Here, Michael wouldn't evenget a half meter off the ground, and would remain airbornea mere .41 seconds. But a game on the moonwould be quite spectacular.

### How to Jump Higher for Volleyball Fast Way to Improve Vertical Jump How to Spike a Volleyball

Today we are just going to talk about verticaljump height and how to improve that number. It's a test that a lot of people get testedon when they go play their sports or go into combines and things like that. We are goingto work on how to improve that height. So I am going to bring in Morgan real quick.Morgan is going to give us a demonstration of a vertical jump. Ah, it's basically a squatjump but just picture that she is testing on a vertical jump and then we'll talk abouttraining progressions and how we are going to go ahead and work on improving that. SoMorgan, just stand tall. When you are ready just squat and get up into the air. Alrightgood. So, it looks pretty simple. She is squatting,

she is jumping up in the air. But we are goingto break this down and we are going to work on improving it. We are going to break itdown into 3 different segments. First we are going to talk about her ability to load properlyor decelerate. She is going to start tall. Too many times athletes have a hard time withthis jump because they can't load their body properly. So usually it is a posture thingor they don't have the mechanics to go ahead and load properly. So we are going to watchMorgan go ahead and just load into a solid base. Load, good. So out of this positiona lot of times what athletes have a hard time doing is that knees will cave in. So, kneescave in and I lose glut activation. I will

lose force, I will lose energy when I go aheadto jump. Go ahead and turn to the side real quick Morgan. This is a good upper body. Sostart tall and go ahead and load. A lot of times athletes will have this sort of roundedback so I am leaking a lot of energy once again into that low back. That will resultin poor performance when I go ahead to jump. One of the biggest things we see too is whenthey load, they will go ahead and load her anterior. Meaning they jump with all theirweight going forward and their heels will be off the ground. So she is going to load,her heels are off the ground. We can see lack of stability here obviously. She is goingto have a hard time getting up in the air