The math behind Michael Jordan’s legendary hang time - Andy Peterson and Zack Patterson
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0:13 - 0:15Michael Jordan once said,
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0:15 - 0:16"I don't know whether I'll fly or not.
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0:16 - 0:19I know that when I'm in the air
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0:19 - 0:22sometimes I feel like I don't ever
have to come down." -
0:22 - 0:23But thanks to Isaac Newton,
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0:23 - 0:27we know that what goes up
must eventually come down. -
0:27 - 0:32In fact, the human limit
on a flat surface for hang time, -
0:32 - 0:36or the time from when your feet leave
the ground to when they touch down again, -
0:36 - 0:39is only about one second,
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0:39 - 0:42and, yes, that even includes his airness,
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0:42 - 0:44whose infamous dunk
from the free throw line -
0:44 - 0:49has been calculated at .92 seconds.
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0:49 - 0:54And, of course, gravity is what's making it
so hard to stay in the air longer. -
0:54 - 0:59Earth's gravity pulls all nearby objects
towards the planet's surface, -
0:59 - 1:03accelerating them
at 9.8 meters per second squared. -
1:03 - 1:09As soon as you jump,
gravity is already pulling you back down. -
1:09 - 1:11Using what we know about gravity,
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1:11 - 1:15we can derive a fairly simple equation
that models hang time. -
1:15 - 1:20This equation states that the height
of a falling object above a surface -
1:20 - 1:25is equal to the object's initial height
from the surface plus its initial velocity -
1:25 - 1:29multiplied by how many seconds
it's been in the air, -
1:29 - 1:32plus half of the
gravitational acceleration -
1:32 - 1:37multiplied by the square of the number
of seconds spent in the air. -
1:37 - 1:41Now we can use this equation to model
MJ's free throw dunk. -
1:41 - 1:45Say MJ starts, as one does,
at zero meters off the ground, -
1:45 - 1:52and jumps with an initial vertical
velocity of 4.51 meters per second. -
1:52 - 1:55Let's see what happens if we model
this equation on a coordinate grid. -
1:55 - 1:57Since the formula is quadratic,
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1:57 - 2:01the relationship between height
and time spent in the air -
2:01 - 2:03has the shape of a parabola.
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2:03 - 2:06So what does it tell us about MJ's dunk?
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2:06 - 2:10Well, the parabola's vertex shows us
his maximum height off the ground -
2:10 - 2:14at 1.038 meters,
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2:14 - 2:17and the X-intercepts tell us
when he took off -
2:17 - 2:22and when he landed,
with the difference being the hang time. -
2:22 - 2:25It looks like Earth's gravity
makes it pretty hard -
2:25 - 2:28for even MJ to get some solid hang time.
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2:28 - 2:33But what if he were playing an away game
somewhere else, somewhere far? -
2:33 - 2:38Well, the gravitational acceleration
on our nearest planetary neighbor, Venus, -
2:38 - 2:44is 8.87 meters per second squared,
pretty similar to Earth's. -
2:44 - 2:48If Michael jumped here with the same
force as he did back on Earth, -
2:48 - 2:51he would be able to get more
than a meter off the ground, -
2:51 - 2:56giving him a hang time
of a little over one second. -
2:56 - 2:59The competition on Jupiter
with its gravitational pull -
2:59 - 3:05of 24.92 meters per second squared
would be much less entertaining. -
3:05 - 3:09Here, Michael wouldn't even
get a half meter off the ground, -
3:09 - 3:13and would remain airborne
a mere .41 seconds. -
3:13 - 3:17But a game on the moon
would be quite spectacular. -
3:17 - 3:20MJ could take off from behind half court,
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3:20 - 3:22jumping over six meters high,
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3:22 - 3:25and his hang time of over
five and half seconds, -
3:25 - 3:29would be long enough for anyone
to believe he could fly.
- Title:
- The math behind Michael Jordan’s legendary hang time - Andy Peterson and Zack Patterson
- Description:
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View full lesson: http://ed.ted.com/lessons/the-math-behind-michael-jordan-s-legendary-hang-time-andy-peterson-and-zack-patterson
Michael Jordan’s legendary slam dunk from the free throw line has been calculated at 0.92 seconds of pure hang time. But how many seconds could Jordan have gotten were he doing the same jump on Mars? Or Jupiter? Andy Peterson and Zack Patterson share the math equation behind hang time.
Lesson by Andy Peterson and Zack Patterson, animation by Oxbow Creative.
- Video Language:
- English
- Team:
- closed TED
- Project:
- TED-Ed
- Duration:
- 03:46