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  • 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。

Michael Jordan once said,

喬丹曾說過,

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B1 中級 中文 美國腔 TED-Ed 喬丹 地心引力 時間 地面 重力

【TED-Ed】喬丹灌籃時間的數學理論 (The math behind Michael Jordan’s legendary hang time - Andy Peterson and Zack Patterson)

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    稲葉白兎 發佈於 2015 年 06 月 19 日
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