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Michael Jordan once said,
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"I don't know whether I'll fly or not.
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I know that when I'm in the air
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sometimes I feel like I don't ever have to come down."
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But thanks to Isaac Newton,
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we know that what goes up must eventually come down.
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In fact, the human limit on a flat surface for hang time,
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or the time from when your feet leave the ground to when they touch down again,
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is only about one second,
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and, yes, that even includes his airness,
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whose infamous dunk from the free throw line
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has been calculated at .92 seconds.
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And, of course, gravity is what's making it so hard to stay in the air longer.
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Earth's gravity pulls all nearby objects towards the planet's surface,
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accelerating them at 9.8 meters per second squared.
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As soon as you jump, gravity is already pulling you back down.
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Using what we know about gravity,
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we can derive a fairly simple equation that models hang time.
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This equation states that the height of a falling object above a surface
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is equal to the object's initial height from the surface plus its initial velocity
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multiplied by how many seconds it's been in the air,
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plus half of the gravitational acceleration
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multiplied by the square of the number of seconds spent in the air.
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Now we can use this equation to model MJ's free throw dunk.
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Say MJ starts, as one does, at zero meters off the ground,
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and jumps with an initial vertical velocity of 4.51 meters per second.
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Let's see what happens if we model this equation on a coordinate grid.
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Since the formula is quadratic,
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the relationship between height and time spent in the air
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has the shape of a parabola.
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So what does it tell us about MJ's dunk?
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Well, the parabola's vertex shows us his maximum height off the ground
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at 1.038 meters,
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and the X-intercepts tell us when he took off
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and when he landed, with the difference being the hang time.
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It looks like Earth's gravity makes it pretty hard
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for even MJ to get some solid hang time.
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But what if he were playing an away game somewhere else, somewhere far?
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Well, the gravitational acceleration on our nearest planetary neighbor, Venus,
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is 8.87 meters per second squared, pretty similar to Earth's.
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If Michael jumped here with the same force as he did back on Earth,
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he would be able to get more than a meter off the ground,
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giving him a hang time of a little over one second.
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The competition on Jupiter with its gravitational pull
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of 24.92 meters per second squared would be much less entertaining.
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Here, Michael wouldn't even get a half meter off the ground,
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and would remain airborne a mere .41 seconds.
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But a game on the moon would be quite spectacular.
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MJ could take off from behind half court,
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jumping over six meters high,
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and his hang time of over five and half seconds,
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would be long enough for anyone to believe he could fly.