The math behind Michael Jordan’s legendary hang time - Andy Peterson and Zack Patterson

翻译人员: Cissy Yun 校对人员: Jenny Yang

Michael Jordan once said,

迈克尔·乔丹曾说过

"I don't know whether I'll fly or not.

“我不知有一天我是否会飞起来”

I know that when I'm in the air

“但我知道当我在空中时”

sometimes I feel like I don't ever have to come down."

“我有时会想永远也不落地”

But thanks to Isaac Newton,

但是伊萨克·牛顿

we know that what goes up must eventually come down.

让我们知道上升的东西总会下降

In fact, the human limit on a flat surface for hang time,

事实上，人类对于平面的滞空时间的极限

or the time from when your feet leave the ground to when they touch down again,

或者说脚离地又触地的时间

is only about one second,

差不多是一秒钟

and, yes, that even includes his airness,

是的，乔丹的

whose infamous dunk from the free throw line

著名的罚球

has been calculated at .92 seconds.

是0.92秒

And, of course, gravity is what's making it so hard to stay in the air longer.

当然，地心引力是使得物体在空中停留不长的原因

Earth's gravity pulls all nearby objects towards the planet's surface,

地心引力会将物体以9.8m/s²的加速

accelerating them at 9.8 meters per second squared.

拉向地球表面

As soon as you jump, gravity is already pulling you back down.

在你跳起得那一刹那， 引力已经开始作用在你身上了

Using what we know about gravity,

对于我们熟以为知的引力

we can derive a fairly simple equation that models hang time.

可以推算出一个可以计算停留时间的简单等式

This equation states that the height of a falling object above a surface

这个等式显示出坠落物体离地面的高度

is equal to the object's initial height from the surface plus its initial velocity

等于物体本身离地的高度加上它最初的速度

multiplied by how many seconds it's been in the air,

乘以在空中的时间（秒）

plus half of the gravitational acceleration

加上½×9.8m/s²

multiplied by the square of the number of seconds spent in the air.

再乘以逗留时间的平方

Now we can use this equation to model MJ's free throw dunk.

现在我们可以用这个等式来模拟乔丹的罚球

Say MJ starts, as one does, at zero meters off the ground,

比如说，乔丹从离地零米

and jumps with an initial vertical velocity of 4.51 meters per second.

跳起时的垂直速度为4.51米每秒

Let's see what happens if we model this equation on a coordinate grid.

来看一下我们在坐标轴上模拟的情况

Since the formula is quadratic,

因为这个等式是一个二次方程

the relationship between height and time spent in the air

高度与时间的关系

has the shape of a parabola.

有一个抛物线的形状

So what does it tell us about MJ's dunk?

所以说，这个等式可以告诉我们什么呢？

Well, the parabola's vertex shows us his maximum height off the ground

这个抛物线的顶点可以告诉我们MJ达到最高的高度是

at 1.038 meters,

1.038米

and the X-intercepts tell us when he took off

而x轴交点可以告诉我们他起跳和

and when he landed, with the difference being the hang time.

落地的时间 之间的不同便是在空中的时间

It looks like Earth's gravity makes it pretty hard

看起来地心引力使得

for even MJ to get some solid hang time.

乔丹很难在空中逗留很长的时间

But what if he were playing an away game somewhere else, somewhere far?

但如果他是在其他地方打比赛呢？ 一个更遥远的地方

Well, the gravitational acceleration on our nearest planetary neighbor, Venus,

在我们的近邻，金星上

is 8.87 meters per second squared, pretty similar to Earth's.

加速度为8.87m/s²，与地球很相近了

If Michael jumped here with the same force as he did back on Earth,

如果乔丹是在金星上以与地球上相同的力气跳起

he would be able to get more than a meter off the ground,

他可以跳的比一米更高

giving him a hang time of a little over one second.

在空中还可以停留地比一秒更长

The competition on Jupiter with its gravitational pull

这场比赛如果在木星上举行的话

of 24.92 meters per second squared would be much less entertaining.

因为其24.92m/s²的加速度会变得无聊

Here, Michael wouldn't even get a half meter off the ground,

乔丹不但跳不到半米高

and would remain airborne a mere .41 seconds.

而且在空中只能停留0.41秒

But a game on the moon would be quite spectacular.

但如果在月球上的话，这场比赛会变得十分精彩

MJ could take off from behind half court,

乔丹可以从中场跳起

jumping over six meters high,

跳到六米高

and his hang time of over five and half seconds,

他在空中可以停留5.5秒

would be long enough for anyone to believe he could fly.

这个时间足够让我们相信他是飞人乔丹