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

Discover the physics behind Michael Jordan’s legendary slam dunk hang time.
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Michael Jordan’s legendary slam dunk from the free throw line has been calculated at 0.92 seconds of pure hang time. But how many seconds could Jordan have gotten were he doing the same jump on Mars? Or Jupiter? Andy Peterson and Zack Patterson share the math equation behind hang time.
Lesson by Andy Peterson and Zack Patterson, animation by Oxbow Creative.
View full lesson: ed.ted.com/less...

[@iandavidson5216]

When a nerd and a jock have to do a group project

[@feili6236]

Ian Davidson Blazian

[@Idisagreethisisnotanon]

Perfect

[@JayzsMr]

And the outcome is a pointless nothing

[@psychotrel]

1000th like

[@TheIcemanthomas]

jock? is this the 50s?

[@ShawnRavenfire]

Okay, we have to make moon basketball a thing.

[@danielkhan1]

It'll take forever to make a 3 pointer though

[@longplays2420]

But half-court dunks are basically travelling, lol

[@MM-tn9cf]

Shawn Ravenfire lol

[@intunetutoring]

Its called Space Jam

[@thomasko1638]

Exactly

[@Daedhart]

Ok, hang time explained. Now explain Hammer time.

[@amused4991]

3 words: Can't touch this

[@diogocampos1181]

lakebytheroad cannot*

[@nutmaster652]

jack miller wow LMAO

[@cjpenaflor9935]

Daedhart ( Me being stereotypical ) It's because he's black, black ppl are good at basketball...that's why he can made those legendary hang times.

[@bookknight]

Daedhart it's hammer time!!!!

[@mooxim]

Someone needs to turn this into a game. Moon basketball sounds awesome!

[@videogyar2]

mooxim It would be more expensive than all NASA projects cost right now.

[@mooxim]

Viktor6665 *videogame

[@oldcowbb]

mooxim hahaha, very funny ambiguity

[@edwinj]

mooxim Play NBA Street Volume 2 haha

[@wiamelabbassi3712]

hahha yeah

[@69edgard]

Lets start a petition to get the NBA to schedule one moon game per season.

[@lutherchuah1342]

E Morales How about we start a petition to have a FRANCHISE on the moon? It can be named the Lunar (year that moon is colonised), like the Philly 76ers

[@asneecrabbier3900]

we should start a government already

[@e.a.c2]

LIKE A SECOND FINALS EACH SEASON!!

[@Diddancing]

time to start inventing the sports of the future. Worthy idea

[@saturn724]

Superman has a hang time of 24/7

[@6iaZkMagW7EFs]

A. Saleh 365

[@owennewo14]

Superman does not obey the laws of gravity, therefore he is immune to hangtime

[@danielam.delyusto5202]

that's less than 3 seconds basic division

[@bip901]

22/7

[@bb1la831]

Ok that is funny 😂

[@cyrus5958]

Well now I really want to see a basketball game on the moon...

[@adityakhanna113]

Or Jupiter? Begin the poll...!

[@666Tomato666]

Aditya Khanna I know! on the moon of Jupiter - Europa!

[@jesseshea9698]

Sam Leduc just don't try shooting or doing layups...

[@thisjointisloose]

The reason why MJ looked like he was in the air for so long during jumpshots was his ability to throw the ball up while he was coming down plus the bending of his knees. It was an unstoppable shot. Simply the GOAT

[@brodyfunk2572]

Well except for wilt chamberlain before you couldn't cross the line on the free throws Wilt was already dunking it from there

[@Johnkoth]

Jim Pollard 6ft 4 was dunking from foul line in practice before Wilt was in college.

[@christianhenry4173]

@@brodyfunk2572 bill Russel, Peter Maverich they all had some impressive verticals.

[@kingdinodragonite3470]

@@brodyfunk2572 yeah but longer legs and a shorter vertical than mj. Not spectacular. People are exaggerating wilt for a long time now.

[@violentabrahamlincoln1395]

Wilt is 7’1 with a 7’8 wingspan with a 46 inch vertical and MJ is 6’6 with a 6’11 wingspan with a 48 inch vertical, it seems pretty amazing that Wilt got 46 inches considering his size

[@duckiebee2831]

*What goes up, must come down* Flys into space Stays away from celestial bodies Stays up till the end of time *wakes up* What the hell?!

[@joseph-kim]

+Duckie bee *hits head* *goes back down* "Oh."

[@pyromaniac6419]

GRAVITY IS A THEROY NOT A FACT NOT SCIENCTIFFICLY SUPPORTED OR PROVEN

[@wlt3585]

pyromaniac 64 wat

[@mr.j_krr_80]

1. If you are orbiting, which is the only way you keep "flying" you ARE actually falling and missing the celestial body. 2. (we don't have the technology or we most probably will never have but) if you are going on an straight line, IT'S IMPOSSIBLE. So pack your jokes and go to sleep.

[@Prince40005]

Y'all remember that hang time at the end of Space Jam ? XD

[@SkyrimHod]

You probably should also have mentioned that for a small enough asteroid, he might not ever come back down and would instead end up in orbit around it or even achieve escape velocity and wind up in orbit around the Sun instead. Would be interesting to calculate exactly how small it would need to be for that to happen.

[@franksierow5792]

I do not think he could go into orbit around an asteroid by simply jumping: he would either not come back down, or would come back down. To orbit he would need some "sideways" velocity. to get into a low orbit, maybe he would be able to run faster and faster until he reached orbital velocity, then lift his feet.

[@45moonprince]

Basically MJ maxed out his vertical for his height

[@tobiaszb]

The equation is about center of gravity. If MJ makes a shot while falling and he pulls up his legs then the jump is longer (in time and distance).

[@waldenli9232]

You made the right comment that most people miss. Cool-sounding high school physics is all about an ideal ball, while MJ has legs and uses his abs to pull them up. Anyone who plays bball and has some hang time know that if you don’t use your abs, you don’t have much hang time to talk about.

[@ethanboyd6885]

Well that answers that - We need to start rostering games on the Moon... it's as simple as that !

[@thatnativeking1333]

“00:45 infamous dunk?” Do you know what infamous means?

[@awaismalik3297]

infamous means famous 😐

[@mohammedavdul5247]

@@awaismalik3297 no it means not popular for good things but bad

[@nonino1644]

@@awaismalik3297 most people don't know the difference.

[@pavanprecious5346]

Fun video, but even more impressive making, kudos to Andy and Zack, I hope you guys keep making more. The best thing that really stood out was the sound, kudos to whoever did it.

[@nikulp68]

I'm sorry, but the equation is wrong. It should be -0.5gt^2 since height and velocity were measured as up being positive. Correct me if I'm wrong. If it was a +, then you wouldn't get the quoted parabola.

[@BoopBep]

Nikul Patel Lol nope. -0.5gt^2 would be used if they had implemented Jordan's final velocity. +0.5gt^2 is correctly used with his initial velocity.

[@pythor2]

Nikul Patel You are correct. A positive square would have an upwards parabola, while a negative square would have a downwards parabola. The negative one is the one we seek if we wish to return to Earth's surface. :)

[@adityakhanna113]

Probably they took "g" to be negative

[@nikulp68]

It's definitely not correct. Let's assume it is correct. That implies the height is strictly increasing. That is wrong. Hence, the initial assumption is wrong. Therefore it should be a -, which makes you wrong also. S=ut+0.5at^2. However, a=-g, since v, s and a are vector quantities and v and s are positive upwards and gravity acts downwards.

[@pythor2]

Aditya Khanna That could be the case if they didn't show positive g values. It's wrong either way.

[@Maluson]

The conclusion of this demonstration is : Actually, Michael Jordan can fly, while everybody else can't. Hope this helps. You're quite welcome.

[@1AmGroot]

I saw the title as "The man behind Michael Jordan's legendary hang time"...

[@Poshur]

1:16 Watch this, Mr.Krabs!

[@arifahmad-7261]

**Ted_Ed : hang time** **Newton :hold my gravity**

[@radiotop6]

*3:11* to *3:24* that beat production is CRAZY son

[@balaramkrishna9]

I was searching for the music credits! (found none)

So space jam was real? :O

[@movement2contact]

why "*infamous* dunk from the free-throw line"?

[@Swagatron22]

whats wrong with it?

[@levi8676]

+Alecs - ''infamous'' is when you are known for something bad.

[@stoicite7]

+Trezor99 Precisely. One bad mofo gave us that dunk.

[@xmaxfactorx]

+movement2contact thats what i was also wondering, theres nothing infamous about it.

[@Twas-RightHere]

+movement2contact I guess he's trying to say 'well known', or 'amazing'.

[@southpenguinjay110]

The problem with the moon part is the fact that it would be a lot harder to accelerate since you’ll just fly up in the air so you’ll have to count that in

[@darkdanne]

g is only 9.82 at the surface. It even varies on different altitudes abobe the surface. It should also be negative acceleration for it follow that form. I think you guys should have checked that

[@YuhaoBoku]

Daniel Björkman g is negative only if you define upwards as positive, it really depends on your chosen coordinate system. I have shown the working outs in Nikul Patel's comment, and what the guy did in the video is correct, no need for re-check.

[@darkdanne]

The hight axis is pointing upwards in the video man

[@YuhaoBoku]

Yes, you're right, but I'm saying it will depend on the chosen direction of positive. But anyways, I have shown the working outs that both cases work. Here is the working out from Nikul Patel's comment: If he defines upwards to be positive, then the value of g would be -9.8, the value of △H would be a positive number, and the value of initial y-velocity would be +4.51. Now from the equation, and the given initial y-velocity values, we would calculate the hang time by taking △H be 0, and work out the two t, then take the difference to get the hang time (just like he stated): 0 = 4.51t - 4.9t^2, rearranging gives: t(4.9t - 4.51) = 0, and so t = 0 and 0.92. Now we consider the other case (should be very obvious now that the other case will also work...): If he defined downwards to be positive, then the value of g would be +9.8, the value of △H would be a negative number, and the value of initial y-velocity would be -4.51. Again using the equation we have: 0 = -4.51t + 4.9t^2, rearranging gives: t(4.9t - 4.51) = 0, and so t = 0 and 0.92.

[@ZipaNipa]

also the animation starting at 0:58 is a bit misleading since it says g=9.8 and shows planets coming towards earth, as if they would be accelerated with the same acceleration. (For others, the further you are the smaller the applied force, following equation G=¥×((m1×m2)÷r^2) where ¥ is the gravitational constant and r is the distance between two objects

[@Jionunez7]

I'd probably only watch basketball if it were played on the moon

[@jesseshea9698]

Jionunez7 Hold this L

[@roreah]

Steph Curry is good at three's, tho. Take a look at it later...

[@GreatBlueKnight]

Peterson and Paterson, a necessary distinction that eliminates the sudden suspicion I had that those two people were somehow related until further investigation.

[@mikjagger3136]

if jordan shoes were as light as today's, mj would be soaring too much

[@jaytona500]

mik jagger i don’t think a couple of ounces would make a difference but you could have said with the designs of the new shoes like the foam and stuff do make you jump higher.

[@mikjagger3136]

@@jaytona500 i agree with you. but i have a jordan 4, i don't know what version it was exactly, but it was heavier, the materials are hard and the weight of it wears you down when sprinting

[@yopappy6599]

Mik Jagger To a year old comment: Certain Jordan's are kinda heavy but they're well mad shoes, and certain ones ain't for hoopin, even if they might look like it. To your point about the shoes being lighter, I think similarly about Jordan's shoes when they first came out, compared to what most other players were wearing at the time, they had to be better than most basketball shoes you could buy at the time. I think there may have been a bit of truth in those Nike commercials poking fun about "it being the shoes" 😂

[@DeSpIsEdIcON100]

Great video, but the formula displayed at 1:34 is actually wrong. It should be -1/2 * gt^2 as gravity is pulling you towards the earth. Then you also get the right picture of the parabola at 2:08 and the correct numerical values. But apart from this mistake, I like the video alot and use it in my lectures!

[@TickedOffPriest]

Considering that Jupiter is a gas planet. I think that Ted-Ed needs to rework those calculations.

[@Twas-RightHere]

+TickedOff Priest The calculations are correct. However in this circumstance we are just hypothetically assuming that you could actually walk on Jupiter.

[@TickedOffPriest]

InfinteGaming101 You know what they say about assuming.

[@Twas-RightHere]

TickedOff Priest No...?

[@TheFlamingdragon2]

"ass"uming

[@abslinzag]

@@Twas-RightHere Actually he looks like he jumps like girl on earth.

[@khaledalzubaidi9228]

"we can use a simple equation" *h=ho+vo(t)+½g(t²)*

[@SidharthMakhija]

He'd probably be crushed on Venus before he could make the jump since it's atmospheric pressure is 90 times that of Earth. :p

[@aweldof]

:P

[@TheVaxruo]

Sidharth Makhija Thank you for your input

[@lordilluminati5836]

+Sidharth Makhija there are plans to colonize the upper atmo of venus, gravity wouldd be similar.you could presurize the court.

[@threalsk]

you know what u have a bright future at ted

[@CookieJari]

Sidharth Makhija How can he jump on jupiter? If I'm not wrong, Jupiter is all gas?

[@thepossimpible3385]

Based off that equation it seems that velocity is the only determining factor, since gravity and initial height is the same for everyone. Does that mean that usain bolt has the greatest hangtime? How does this equation apply to long-jumpers, since the WR is almost 9m, was their velocity just that much greater than MJs?

[@alex2005z]

The equation is wrong here. This is bc MJ isnt a ball. He is a human. By pulling his legs up he changes his center of gravity, thus changing hang time

[@chowtieshan1361]

Finally I can say someone can dunk from three pointer

[@markdaniel9657]

Upvoting for that bop of a music

[@robertconrad2855]

In basketball, "hangtime" refers to the time your feet are off the ground. Clearly Jordan is off the ground much longer than .98 sec. Is hangtime in this video referring to the time spent at max height? I'm 45 year old dude and can count "one one thousand, two one thousand" while in the air. So I'm certain this .98 calculations is something else.

[@EugeneGolden]

But that depends on initial velocity? How do we determine that? Are we using an Olympic record as the maximum? Are we using the point at which the leg bones would break? I get you are trying to be succinct but just a single sentence of where you got the maximum time of 1 second would've made this video so much better.

[@gaminwatch8203]

If hang time is how long you hang on the basket, wouldn't the limit only be how long your arm can hold you?

[@WhiteBloggerBlackSpecs]

Even on the moon he'd take it personally

[@deep5468]

You can explain "hang-time", but you cannot explain "Jordan time". One, two, three people go up to try and block the shot from Jordan, means one, two, three people will not. Your mortal mind was not meant to comprehend his "airness" moves, but to study, imitate, and be humble and proud of those who seen him do them.

[@DJMarkCorneliusThaDon]

We learned this back in the day. Michael Jordan overcomes the acceleration of gravity by the application of his muscle power, in the vertical plane, thus producing a low altitude earth orbit.

[@XxmattitudexX]

should be pretty easy for the moon hoax debunkers or theorist to calculate the height the jumps the astronauts made in the moon footage and see if it lines up with the moons specific gravity. certain height should equate to a very specific fall time

[@__-nt2wh]

XxmattitudexX They'd need the impulse the astronauts receive.

[@yanniskarageorgiou3573]

Michael Jordan was only 8% off the max human limit those guys were probably 50%

[@menzoznem]

wouldn't his velocity at the beginning change on other planets since he is heavier or lighter?

[@ShietEverywhere]

If this video had come out while he was in his prime he would have found a way to disprove it. #GOAT

[@FcBarcelonaKid]

the background music was really nice

[@dimitrisg1374]

1:01 The MEDIAN is 9.8 m/s^2 and it only applies to masses on the surface of the earth... So it doesn't attract every object with this acceleration because the radious of the distance from the earth's centre is greater

[@ChaiRack]

The actual differences between values of gravity due to ones changing radius is minute, and if you truly care so much about minute differences you would note the value is 9.81m/s^2

[@dimitrisg1374]

manny lemos sure, no doubt about that, But when they show whole planets as objects accelerated with 9.8 m/s^2 due to earth's gravitational force, it becomes a bit of a fallacy to say that everything is accelerated at this ratio

[@NotTakenGreatName]

All very interesting, but um couldn't you just watch a video and use a stopwatch to see how long he was in the air?

[@ZachLau00]

With the thing about jumps on other planets, it neglected the fact that he would also be able to have a much higher initial velocity on the moon because it would be easier to accelerate vertically with less weight, meaning he could jump even farther

[@user-ci2lg1lw5b]

수학과 멀게 느껴졌던 체육도 수학에 눈으로 바라보는 시각을 얻었습니다. 정말 재미있었습니다. 다른것에도 숨겨진 과학이 있는지 생각해 보기도하고 새로운 시각으로 바라보게 되었습니다. 재미있는 시간이 되었습니다. 감사합니다.

[@robhughes8198]

Is the ‘1 meter’ limit due to the specific dunk that you chose or just over simplifying the math? Because it’s well known that Jordan can jump over 1.2 meters.

[@dinogirl9055]

Another reason why some basketball players are so good is that their hands show the gooden ratio's measurement or similar to it.

[@mannyneva1960]

41” off the ground jumping from the free throw line....this is why MJ says he’s a leaper

[@isaacadams6898]

we can easily model this equation *starts to panic cause it's the weekend and that equation was complicated af*

[@thalespro9995]

0:42 do u know what infamous means ted Ed

[@SKyrim190]

Kind of misleading how the time coordinate mapped exactly into the forward distance of the animation. They are different measurements

[@zackzaki6695]

tbh, this video make me remember about cristiano jump against sampdoria

[@0-Elias-0]

Ted-Ed Question: How did you come up with the 4.51 m/s for initial velocity?

[@0-Elias-0]

Could you share the function?

[@omarsayed7804]

Wait a second Cristiano Ronalodo acheived a hang time of 1.5 seconds on a jump that was 2.65 m high

[@alex2005z]

Thats because this video is wrong. Due to the simple fact that humans arent balls. By pulling your legs up you change your center of gravity, thus increasing hang time. There are a few more technics for that as well

[@ChristopherPlays]

What's the name of the song starting from 3:05?

[@akash1457]

Do you guys have a recording of MJ's dunk from side view I'm doing some calculations on the dunk from the raw video but all the ones I found were of a moving camera.

[@ritvikdutta4824]

What about Dr J, Serge Ibaka and Zach LaVine, who also dunked from the free throw line? Especially Dr. J

[@bronze_summer723]

I came here to learn how to be decent at basket ball 😂

[@threalsk]

oh no look at his dp he didnt

[@BaBooTubeVideos]

Go away, this is a nerd channel, not a basketball vine moron channel. We don't want you here.

[@ultramariogod]

If Michael Jordan trained in a strong gravity planet like Jupiter and then traveled to earth which has a weaker gravity he would literally fly, he would need a lot of force to hang for one second in Jupiter but that force would make him hang on Earth for around 2 seconds

[@shko1259]

I think a gas planet would make him fall into its core

[@shko1259]

But if he trained in the moon, he would be really weak.

[@haoxinchao7479]

the thing is with lower gravity the velocity and acceleration of the mbasketball player would also increase.

[@Fluffypringle]

interestingly enough I'm doing a presentation on this exact topic for physics and when using the equation and calculating height and air time my numbers for Michael on Jupiter are backward I get a height of .41m and a time of.36 seconds

[@roidroid]

What about the angle at which you jump tho? If you jump straight up, then you get the max height and max hangtime. But if you jump forward, then that takes away some of the energy from your jump's height, lowering your hangtime. Michael's "infamous jump from the free throw line" obviously wasn't a straight vertical jump, if he were to reach the net.

[@jackxiao9702]

what's the name of the song?

[@Majinbeck_exe]

What is the music thought the video

[@Lopsinho]

Did they take into account the difference in weight? Or assuming the jumps force a constant?

[@Kryptolistic]

So this explains the Space Jam half court shot was shot at the moon, we just need to figure out the arm extension. It was probably a TP-Link wristband, the blue one.

[@jenniferfas8097]

This video would definitely grab the students' attention in class. Great real world problem!

[@ikram21norazam44]

the music fits perfectly with the video :)

[@samsungsiphone4354]

Can you explain your explanation?

[@orobiavlogs5214]

How can u explain gravity for the light creatures like butterfly?

[@alex2005z]

They get pulled down like everyone else. They just fly back up

[@jose_glz]

OMG! Just like in "Space Jam".

[@HolgerBrandsmeier]

what about the role of the initial acceleration? To witch degree could humans vary that?

[@williamzame3708]

A maximum height of 1.038 meters (41 inches) seems not quite enough; MJ supposedly had a vertical leap of 48 inches.

[@xaustinx15]

Wait at 00:58, doesn't gravity weaken the farther away you are? Or is that just the force that does that?

[@alex2005z]

Its not a significant change from the center of the earth

[@kirbymarchbarcena]

Add a double somersault before dunking and his airness will be more epic you'll believe he can fly.

[@lessgoo3428]

That are very simple maths. We learned then in second grade of junior high school

[@SuperSuperswag101]

what about clyde "glide" drexler?

[@user-go4wi4lx7q]

I wish I can see him again😢

[@tomarik]

I love Ted-Ed

[@754759119]

Does hangtime have to do with body weight? a feather drops slower than a stone when thrown to the same height.

[@gaboqv]

not dependant in weight at all, what makes the time different for stones and feathers is what i think in english you call "drag"

[@754759119]

Alejandro Quinche if shaq and iverson jump to the same height, who land first?

[@alex2005z]

It doesnt have to do much. Air resitance isnt very relevant compared to a human's weight.

[@brainboxanky1729]

@Ted_Ed #correction at 2:35 Nearest planet to earth is not Venus but Mercury (if you take distance to be the average distance over an year) may refer here👇 kzbin.info/www/bejne/iabQdXuZo6iFq7c

[@danielbabalola7450]

What about long jump records?

[@ayammayaartist]

I'm surprised of the lack of Space Jam comments.

[@prathmesh8482]

Ronaldo jumped to the height of 2.56 metres against Sampdoria and his hang time in the air was 1.5 seconds...........

[@gitgudnga]

what if u do a roundoff into a double back

[@doublehelix911]

Shouldn't it be mentioned that air resistance was not considered?

[@magicatt1]

i think it should be -0.5gt^2

[@VarunSingh000]

+magicatt1 No you just take the value of g with a negative coefficient. (Defining it as gravitational retardation rather than acceleration.) Keeps the equation simple. Changing it everywhere would make the maths very confusing.

[@unthoughtof7338]

I was waiting for a way to dunk easier

[@ketan6182]

Lol if there were NBA matches on the moon, All star games would take a whole different meaning.

[@ifeelblue8867]

Wait i cant seem to get the same results using the equation

[@WOW-jw4du]

So if someone jumps bout 30inches off the ground then someone who jump 43inches off the ground your telling me they would have the same hang time🤔idk how it works

[@achyutanm2351]

S=ut+1\2at2.(at2 is at squared)

[@prolarka]

I expected this to be about the feeling of time slowing down for the player and its biophysical reasons...

[@zixiong681]

now i wanna see astronauts play basketball

[@bamb8s436]

Well, Zach Lavine's dunk at an NBA dunk contest was the longest ever, so you should have referred him instead of Jordan.

[@franciscopizarro5424]

Lambros_pap ότι να 'ναι Jordan had a 48 inch vertical

[@bamb8s436]

@@franciscopizarro5424 Jordan have never dunked behind the ft line though.