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

喬丹傳奇的滯空時間背後的數學 - Andy Peterson 和 Zack Patterson

譯者: Zongzhen Yang 審譯者: Wang-Ju Tsai

Michael Jordan once said,

喬丹曾說過，

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

“我不知道我是否會飛，

I know that when I'm in the air

但我知道我一旦在空中，

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

有時我感覺我再也不會下來。“

But thanks to Isaac Newton,

但是透過牛頓的定理，

we know that what goes up must eventually come down.

我們知道了飛起來的東西最後一定會掉下來。

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

事實上，人類離一平面的滯空時間，

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

或者從雙腳離開到再回到地面的時間，

is only about one second,

差不多只有一秒，

and, yes, that even includes his airness,

而且，是的，甚至包括了喬丹的滯空，

whose infamous dunk from the free throw line

他著名的罰球線起跳灌籃

has been calculated at .92 seconds.

經過計算是0.92秒，

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

而且，當然，重力使滯空時間很難延長。

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

地心引力把所有東西拉向地球表面，

accelerating them at 9.8 meters per second squared.

以9.8米每平方秒加速。

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

一旦你起跳時，重力就把你往下拉。

Using what we know about gravity,

根據我們對重力的認知，

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

我們可以推導出一個相當簡單， 可以計算滯空時間的公式。

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

這個公式說明落體到地面的高度

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

等於這個物體最初的高度加最初的速度

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

乘以滯空的時間，

plus half of the gravitational acceleration

加上一半的重力加速度

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

乘以滯空時間的平方。

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

現在我們可以使用這個公式 來求出喬丹的罰球線灌籃。

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

當MJ一起跳時，他與地面的距離為零，

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

他最初的垂直速度是每秒4.51米。

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

讓我們看看如果我們 把這個公式放到坐標會發生什麼。

Since the formula is quadratic,

因為這是一個二次方程式，

the relationship between height and time spent in the air

高度和滯空時間的關係

has the shape of a parabola.

形成了一個拋物線。

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

這能告訴我們什麼有關MJ的灌籃的事？

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

那麼這個拋物線的頂點 告訴我們他離地面的最大距離

at 1.038 meters,

是1.038米，

and the X-intercepts tell us when he took off

而且x的截點告訴我們他起跳

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

和落地之間的時間是滯空時間。

It looks like Earth's gravity makes it pretty hard

看起來地心引力讓事情變得困難

for even MJ to get some solid hang time.

甚至讓MJ無法得到更長的滯空時間。

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

但是如果我們在很遠很遠的地方比賽 結果會有何不同？

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

離我們最近的星球鄰居金星的地心引力是

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

8.87米每平方秒，這與地球的地心引力類似。

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

如果喬丹用和在地球上一樣的力跳，

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

他會跳得離地面一米多一點，

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

並給他比一秒還多一點的滯空時間。

The competition on Jupiter with its gravitational pull

在木星上的比賽，因為它的引力

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

是24.92米每平方秒，會沒有那麼有趣的。

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

在那裡，喬丹甚至都不能離地半米，

and would remain airborne a mere .41 seconds.

而且滯空時間也僅僅只有0.41秒。

But a game on the moon would be quite spectacular.

但是在月亮上的比賽會相當的令人驚嘆。

MJ could take off from behind half court,

MJ可以從中場線起跳，

jumping over six meters high,

跳六米高，

and his hang time of over five and half seconds,

而且有五秒半的滯空時間，

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

足夠讓任何人覺得自己可以飛。