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

Matematika iza legendarnog skoka Majkla Džordana - Endi Piterson i Zek Paterson

Prevodilac: Mile Živković Lektor: Anja Saric

Michael Jordan once said,

Majkl Džordan je jednom rekao:

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

"Ne znam da li ću poleteti ili ne.

I know that when I'm in the air

Znam da kada sam u vazduhu,

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

ponekad se osećam kao da nikada ne moram da siđem."

But thanks to Isaac Newton,

Ali zahvaljujući Isaku Njutnu,

we know that what goes up must eventually come down.

znamo da sve što se popne nekada mora i da siđe.

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

Zapravo, ljudsko ograničenje za lebdenje na ravnoj površini,

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

ili vreme od kada vaša stopala napuste zemlju do kad je ponovo pipnu

is only about one second,

iznosi samo oko jedan sekund,

and, yes, that even includes his airness,

i da, do uključuje i njegovo vazduhovisočanstvo

whose infamous dunk from the free throw line

čije je čuveno zakucavanje sa linije slobodnog šuta

has been calculated at .92 seconds.

izmereno na ,92 sekunde.

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

Naravno, gravitacija je ta koja otežava da duže ostanete u vazduhu.

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

Zemljina gravitacija sve obližnje predmete vuče ka površini planete

accelerating them at 9.8 meters per second squared.

i one ubrzavaju na 9,8 metara po sekundi na kvadrat.

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

Čim skočite, gravitacija vas već vuče nadole.

Using what we know about gravity,

Koristeći ono što znamo o gravitaciji,

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

možemo izvesti prilično jednostavnu jednačinu za model lebdenja.

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

Ova jednačina kaže da je visina objekta u padu iznad površine

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

jednaka prvobitnoj visini objekta od površine plus prvobintnoj brzini

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

pomnoženo se brojem sekunda koliko boravi u vazduhu,

plus half of the gravitational acceleration

plus polovina gravitacionog ubrzanja

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

pomnožena sa kvadratom broja sekundi provedenih u vazduhu.

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

Sada možemo napraviti model Džordanovog zakucavanja uz ovu jednačinu.

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

Recimo da Džordan, kao i svi, počinje sa nula metara na zemlji

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

i skače sa početnom vertikalnom brzinom od 4,51 metara po sekundi.

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

Da vidimo šta se desi ako ovu jednačinu prebacimo u koordinatni sistem.

Since the formula is quadratic,

Pošto je formula kvadratna,

the relationship between height and time spent in the air

veza između visine i vremena provedenog u vazduhu

has the shape of a parabola.

ima oblik parabole.

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

Šta nam to govori o Džordanovom zakucavanju?

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

Najviša tačka parabole pokazuje nam njegovu maksimalnu visinu

at 1.038 meters,

na 1,308 metara

and the X-intercepts tell us when he took off

a presek X-ose govori nam kada je skočio

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

i kada se spustio, dok vreme lebdenja čini razliku.

It looks like Earth's gravity makes it pretty hard

Čini se kao da Zemljina gravitacija prilično otežava Džordanu

for even MJ to get some solid hang time.

da bude u vazduhu neko vreme.

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

Ali šta kada bismo igrali u gostima negde drugde, negde daleko?

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

Pa, gravitaciono ubrzanje na našem najbližem susedu, Veneri,

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

iznosi 8,87 metara po sekundi na kvadrat, prilično slično Zemlji.

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

Ako bi Majkl ovde skočio istom silom kao na Zemlji,

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

uspeo bi da skoči više od metra od tla,

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

čime bi dobio vreme u vazduhu nešto preko jedne sekunde.

The competition on Jupiter with its gravitational pull

Takmičenje na Jupiteru sa njegovom gravitacionom silom

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

od 24,92 metra po sekundi na kvadrat bilo bi mnogo manje zabavno.

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

Ovde se Majkl ne bi odvojio ni pola metra od tla

and would remain airborne a mere .41 seconds.

i u vazduhu bio ostao samo ,41 sekundu.

But a game on the moon would be quite spectacular.

Ali utakmica na mesecu bila bi spektakularna.

MJ could take off from behind half court,

Džordan bi mogao da skoči iza polovine terena,

jumping over six meters high,

do šest metara u vazduh,

and his hang time of over five and half seconds,

gde bi proveo preko pet ipo sekundi,

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

što bi bilo dovoljno da bilo ko poveruje da on može da leti.