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迈克尔-乔丹曾经说过—— Michael Jordan once said,
"我不知道我能不能飞 "I don't know whether I'll fly or not,
(但)我知道的是当我身处半空之中 I know that when I'm in the air,
有时候我感觉自己永远不会下落" sometimes I feel like I don't ever have to come down."
但是多亏了艾萨克-牛顿 But thanks to Isaac Newton,
注: 牛顿 著名的物理学家 提出了万有引力定律
我们知道 上升的物体最终一定会下落 we know that what goes up must eventually come down.
事实上 在平地上人类的滞空时间极限 In fact, the human limit on a flat surface for hang time
或者说从你双脚离开地面到它们再次触碰地面的时间 or the time from when your feet leave the ground to when they touch down again
仅仅约为1秒钟 is only about one second.
没错 就连"飞人"也是如此 And yes, that even includes His Airness,
注: His Airness为乔丹的外号 即飞人
他著名的罚球线扣篮已经被计算出(滞空)0.92秒 whose infamous dunk from the free throw line has been calculated at 0.92 seconds.
当然 重力是使得在空中滞留困难的原因 And, of course, gravity is what's making it so hard to stay in the air longer.
地球的重力将附近所有的物体拉向行星的表面 Earth's gravity pulls all nearby objects towards the planet's surface,
加速度为9.8米每平方秒 accelerating them at 9.8 meters per second squared.
你跳起的一瞬间 重力就已经将你拉回 As soon as you jump, gravity is already pulling you back down.
利用我们关于重力的知识 Using what we know about gravity,
我们可以推导出一个描述滞空时间的相当简单的方程 we can derive a fairly simple equation that models hang time.
这个方程表明了地面上方即将下落的物体的高度 This equation states that the height of a falling object above a surface
等于 is equal to
物体距离地面的初始高度 the object's initial height from the surface
加上它的初始速度与滞空时间的乘积 plus its initial velocity multiplied by how many seconds it's been in the air
再加上重力加速度与滞空时间的平方的乘积的一半 plus half of the gravitational acceleration multiplied by the square of the number of seconds spent in the air.
现在我们可以用这个方程去对乔丹的罚球线扣篮进行建模 Now we can use this equation to model MJ's free throw dunk.
假设乔丹起跳的初始高度为0m 跟正常人一样 Say MJ starts, as one does, at zero meters off the ground,
以4.51米每秒的初始速度起跳 and jumps with an initial vertical velocity of 4.51 meters per second.
让我们看一下如果我们将这个方程放到坐标网格中会怎样 Let's see what happens if we model this equation on a coordinate grid.
由于方程是二次的 Since the formula is quadratic,
高度和滞空时间之间的关系具有抛物线的形状 the relationship between height and time spent in the air has the shape of a parabola.
那么对于乔丹的扣篮 这告诉了我们什么呢? So what does it tell us about MJ's dunk?
那就是 抛物线的顶点向我们展示了他的离地最大高度为1.038米 Well, the parabola's vertex shows us his maximum height off the ground at 1.038 meters.
而X值告诉我们他起跳以及落地的时间点 And the X-intercepts tell us when he took off and when he landed,
注: X-intercept为函数图形与X轴的交点到原点的距离
二者之差即为滞空时间 with the difference being the hang time.
看样子地球的重力使得哪怕乔丹要得到不错的滞空时间也很难 It looks like Earth's gravity makes it pretty hard for even MJ to get some solid hang time.
但是 如果他是在其它远远的地方打一场客场比赛又会怎样呢? But what if he were playing an away game somewhere else, somewhere far?
呃 我们最近的行星邻居金星的重力加速度为8.87米每平方秒 Well, the gravitational acceleration on our nearest planetary neighbor, Venus, is 8.87 meters per second squared,
与地球的十分接近 pretty similar to Earth's.
如果乔丹在这里以与在地球时一样的力起跳 If Michael jumped here with the same force as he did back on Earth,
他跳起的高度会超过一米() he would be able to get more than a meter off the ground,
可以得到稍微超过一秒的滞空时间() giving him a hang time of a little over one second.
在重力加速度为24.92米每平方秒的木星上的比赛 The competition on Jupiter with its gravitational pull of 24.92 meters per second squared
则会缺乏娱乐性很多 would be much less entertaining.
在这里 乔丹的跳起高度甚至不会超过半米(0.36m) Here, Michael wouldn't even get a half meter off the ground,
并且滞空时间仅有0.41秒 and would remain airborne a mere 0.41 seconds.
但是 在月球上的比赛会非常地壮观 But a game on the Moon would be quite spectacular.
乔丹能够在半场以外起跳 MJ could take off from behind half court,
跳起六米多高 jumping over six meters high,
而超过五秒半的滞空时间 and his hang time of over five and half seconds
足以让任何人相信他会飞 would be long enough for anyone to believe he could fly.
注: I Believe I Can Fly为乔丹主演的电影《空中大灌篮》的主题曲
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