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  • 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.

Michael Jordan once said,

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TED-ED】マイケル・ジョーダンの伝説的なハングタイムの裏にある数学 - アンディ・ピーターソンとザック・パターソン (【TED-Ed】The math behind Michael Jordan’s legendary hang time - Andy Peterson and Zack Patterson)

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    稲葉白兎 に公開 2021 年 01 月 14 日
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