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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.


