Parametric equations 1 | Parametric equations and polar coordinates | Precalculus | Khan Academy

[@ScrawnyCFB]

I have my Calc 2 final tomorrow morning at 7 am and I would absolutely love to be in that car driving off of the cliff

[@ScrawnyCFB]

@@Ryan50Ryan I ended up getting a 95%, which was a MASSIVE surprise

[@aadhityakumaran2016]

Well That's a world with no air, you would have died without driving off

[@lelo8244]

@@ScrawnyCFB congratulations ❤️❤️❤️❤️❤️

[@SortaFresh]

@@ScrawnyCFB yayy nice job

[@hozayrodriguez8968]

❤❤❤❤❤😂😂😂😂

[@codyhufstetler643]

as a mechanical engineering student, relating this to physics helped immensely. thank you.

[@Wasoska]

Same

[@bychen5011]

It's been 8 years. How has ur life changed?

[@assemsarimova4969]

@@bychen5011 i wanna know too

[@godvegito3686]

How has your life changed?

[@probably_meg]

This man has literally saved my life in high school. And will still be there in college...haha I wish every teacher of mine taught like him, learning is SO EASY.

[@real_john_doe]

Why am I being taught this at the very end of Calc 2?

[@Lucky10279]

Same here. I'm confused as to why this video is categorized as precalc.

[@Wasoska]

Same

[@rayyfire5738]

@@Lucky10279 this topic is involved in precalculus textbooks

[@Lucky10279]

@@rayyfire5738 Clearly, it varies by curriculum, as a lot of other people said they're learning it a lot later.

[@rayyfire5738]

@@Lucky10279 the curriculum is not the textbook, of course it would vary by curriculum

[@Direwolf56]

"And this car is not just sitting on the cliff, its driving off of it." I love Sal that much more now.

[@Gelenvader3]

when i saw projectile motions i got so triggered :( ptsd got me

[@drutledge884]

Why is this video more helpful than my pre-cal teacher?

[@Bush21122]

I love this dude .. lol thanks Sal

[@EsaldaH]

@ForeverWiked acceleration : ax=0, ay= -g (gravitational acceleration on earth) You integrate the acceleration to get the velocity -> velocity : vx= 5, vy = -gt (don't forget the initial conditions, here the velocity at t=0) Then you inegrate the whole thing again to get the position -> position : x=5t+10, y= -gt²/2 + 50 with g~10m/s² Again, initial conditions. Position at t=0.

[@ringo38825]

brilliant! I'm a math major and a Trig tutor and this lecture has given me a new method of teaching parameters.

[@AliceWeeksAli]

as a Brit this guys voice and positive attitude is a welcome break honestly lmao

[@niconikko]

For God so loved the world, he gave us Mr. Khan. Sal is the next savior!! Thumbs up if you agree.

[@Ccccccccccsssssssssss]

Thanks, this was really helpful in understanding WHY we're learning parametrics!

[@theadel8591]

Your comment is new

[@mysticmonk3456]

Ah yes, the very practical "driving off a cliff problem" ; my favorite.

[@Jonnemanne]

I really like these clearer high-def videos ! It'd be great if you could redo the projectile motion videos in HD. In my opinion there's nothing better for the beginning/struggling physics student than clear, easy-to-follow AND read fundamental videos. :) thanks Sal, you've done an awesome job ! Greetings from Finland !

[@carlosr6547]

Finally!!, somebody that can explain it so simply, thank you so much

[@cedricfrancis5662]

This is a very good video on the concept of parametric equations. I've known about them for some time now but couldn't link them to everyday life until I came across this video. Now I won't forget about parametric equations, because i now grasped the concept fully, thanks to this video.

[@Macdawg347]

I love your teaching style, very good job!

[@Travoid]

Pa-RAMETER. Parameter. ...pa-rameter.

[@binayakchowdhury405]

Nicely explained. Thanks to You tube and Khan Academy.

[@HockeyMan-kd7yj]

Exactly what I needed thanks!

[@stealth834]

I am a math tutor and your videos provide me with another method to get information across to students. Thanks for the great work!

[@ssj4edits840]

Legends say you're still giving informations to students...

[@Raiyun166]

I learnt it during precalc. But naturally it applies in calculus too.

[@winstonlee3687]

ratio

[@Reydriel]

So that parameter 't' is like a third variable or a third axis? If you used a three-dimensional graph it would be the same thing, right? (if you look at it from the plane of the x and y dimensions only, of course)

[@MountainNZ]

Oh God. Thank you. Finally I see why. Why is this not the first thing we get taught?

[@AliveDog]

me too man. 3 weeks till final and I'm stuck on this shit.

[@physicsboi1744]

lol its been 9 years, do you still use maths often in ur career? Thx just asking :)

[@TuscaniManiac]

may god bless you man..just keep doing those videos ..they're super helpful !! 5 stars !

[@theodoresweger4948]

I loved putting this in my HP prime using the parametric app, thanks and I have just been studying kinematics beautiful thank you.

[@davenhunt]

The mass would be used in calculating the force on the car (or the ground), or some other information. If the car had no mass, gravity would not affect its motion. In a vacuum, all masses would behave in exactly the same way, so the equation covers objects of any mass.

[@klotweev]

@restituted Because, he set the equation equal to zero(the y axis being the height(when would the car be at zero height, or hit the ground)), and the equation was then 0 = 50 - 5t^2. So, he had to figure out what t would have to be for 50 - 5t^2 to equal 0. If t = the square root of 10, then the square root of 10 squared = 10. 50-5(10) = 0. So at the square root of 10 seconds, the car hits the ground.

[@punaydang2948]

can someone explain at 4:24 from where t^2÷2 came?

[@topdown4705]

I believe it's in his projectile motion videos www.khanacademy.org/science/physics/one-dimensional-motion/old-projectile-motion/v/projectile-motion-part-1

[@shamikpatro]

Generally speaking, if you integrate acceleration twice with respect to time, you should get an equation with (t^2)/2 as one of the terms. Here's a helpful crash course video on Integrals (kinematic equations) if you're interested in finding out why: kzbin.info/www/bejne/oH2tfYuhlpeqe68

[@bensculfor9706]

Such a good video. We have been learning about this stuff in further maths but we were never told about when this stuff could be used.

[@microhaxo]

@restituted 0 = 50 - 5t^2 Solve for t.

[@CJEF1996]

this is the wrath of khan

[@JordanMedina]

thanks man this cleared things up!

[@nas-cf1wy]

If you want to know when the car exactly hit the ground. Solve for t using y=0 and find value of t

[@1Rab]

how on earth do you draw such perfect lines~!

[@Atson3003]

Rab the software locks the cursor in a straight line ....

[@agjehj]

wow.. you seem to be enjoying this. a lot. and pretty colors :)

[@shibbyness]

THIS IS REALLY GOOD!

[@akbvr]

Mr thompsons class ftw!

[@RSA_Shock]

Hey this was made on my birthday

[@jacoman1234567]

Thanks for clearing out my mistake :)

[@Tucktasticationister]

I made my KZbin account to listen to free music.... I never thought I would subscribe to a math teacher! haha

[@tpstrat14]

Well I think I may ditch my textbook. He’s such a great teacher !

[@Lyxtwa]

I didn't know that there was a specific name for this. This would have been kind of useful to know before working with Rates of Change differentials.

[@stramelhouse]

woah. Thank you so much.

[@alihajjar8]

"This is WHY" period

[@zack_120]

8:24 - Sal's visual scaling accuracy needs to improve in order to make this channel even better :)

[@00JosefK]

The car off the cliff problem always makes me think of Toonces the driving cat.

[@ClickGoesTheMouse]

Why does he use t^2/2 (4:25) ?

[@veralau93]

thanks that was fantastic!

[@RachelSadoff]

THANKYOUTHANKYOUTHANKYOU

[@Naruto0519]

@HoorayforOranges True true! It's not confusing like teachers always make it seem!

[@mamishmash]

try the whole of vector calculus in 4 days!

[@Danielxyoon]

i was wondering..do you use the mouse to draw these things or is it like a smart board?

[@ollera18]

can someone please link the video that explain the t^2/2 for the y(t) equation??

[@monahusseini6876]

usually the equation of the curve of an accelerating object is x=1/2a.t^2+Vi.t+Xi , where you can substitute x with any dimension and i is the initial point. This is a physics equation related to a(acceleration), v(velocity) and position(x,y,z,...)

[@findo9615]

@@monahusseini6876 u think he waited 5 years for an answer lol

[@Vathanaization]

Thanks

[@dbmasters]

@Lamboragon if you don't like the video, find another one that takes your fancy out of the 396 other videos on parametric equations.

[@rommelram1lovr2]

Hey!...Sal...More power!...(is it ok to say then that the Projectile Motion videos are mathematical analyses of one-dimensional variables (h or delta D)...the 2-Dimensional Projectile Motion...of two-dimensional variables (delta D & Ave. Velocity)...the Prametric Equation...of three-dimensional variables (x, y, & t) or are they...Alll...3D analyses???)...tnx! :D

[@bboydjoe]

@mechwarreir2 its in calc too, (calc bc to be exact)

[@NexFuturex]

I really wonder thathow to know salman khan all of things . really thanks.

[@arandompersononyoutube3739]

2:06 Assuming that we are in a planet and there is no air and no forces like friction etc ,we are in vaccum 4:15 how gravity comes? Please could you please explain the topic , I can't understand clearly.

[@adamsowinski9297]

did you resolve it, i dont get it too

[@mitchwulfman]

haha, khan always has my back.

[@davidd7327]

I have the worst calculus teacher ever!!! Thumbs up:)

[@jacoman1234567]

Does the mass of the car have any influence on the downward motion? Or is it taken in by the projectile curve formula?

[@Joesire]

yes

[@bamfan151]

Anyone else got a test they aren't ready for? lol

[@LoneAssassinX]

Great!!

[@saharaicaldera331]

"We're on a planet that has no air.. we're in a vacuum" LOL why was that funny to me

[@toasty4000000]

parameter. parameter. parammmmeterrrr. hahaha

[@williamjohnson9248]

im 11 and i can understand this and my friend is a ginesous (and i misspelled that sorry for my compertance ) and he diden't understAND IT ;)

[@benjamincordes207]

Thank you so much. Now i finally get it.

[@rolfch1p]

nice videos!

[@ubong-abasiakpan1771]

Y is acceleration due to gravity negative (-10m/s²) Based on equations of motion, for any body moving downwards (g) is positive, and if it's projected upwards it's magnitude becomes negative cause it's acting in an opposite direction to (g) So sir explain why 10m/s² is negative Cause am confused at that point 😕

[@paperorpaper]

Sal can you please make a basic gemonetry video? I was going to start practicing but I have no idea what to do.

[@braineedly7543]

at 4:21 why over 2? Where did it come from?

[@CuteAnimeJunkie]

Thanks so much! This really helped me n_n

[@purplefire5]

all right so i have some questions and any help is appreciated! *I'm just learning this and so far I've really only seen the conventional f(x)= x + a (or trig/rational functions etc.) basically where y or f(x) is on one side and the equation is on the other and that suffices to describe the function. But I've never seen two equations describe a single function and i want to know why this is suddenly happening (i get that the two equations show where the object with respect to time) it's just a function has never been described with two equations for me and i feel like I'm missing something here why is this extra description needed (I know it's a weird question) *Also what is a parameter exactly, is it the same thing as a variable, like for an equation F(x)=cos2x is x the parameter????? *Finally, under what conditions/or what type of function do we need something like this where we need a pair of equations to describe the function? I haven't gotten my textbook yet and all I have to go off of are my notes so i would really appreciate the help THANKS AGAIN!

[@Visiorex]

Let's make a table here... let's make a TABLE.

[@r0b0bert]

Khaaaaaaaan!

[@thelsdj]

No, mass has nothing to do with acceleration of gravity. A ping pong ball and a golf ball would have the same path if there was no air resistance.

[@AmidSedghi]

midterm in 2 day - god bless

[@tylerguitar75]

I came here because of my Cal 3 textbook yet this video says precal... Uh, what?

[@UdyKumra]

+Tyler Yates I came here from my Advanced Algebra Honors class...

[@xavierdingeldein5268]

I came here from my Theoretical Physics class...

[@bythetimeyoufinishedreadin9083]

People, people.... math is like the crying baby on an airplane...its EVERYWHERE, no matter where you go!

[@rinaberman7686]

^Well said.

[@GueVonez]

I came here from my phd in mathamatics honors super duper high level secret school of big boys

[@HockeyMan-kd7yj]

How do you write so well with a cursor?

[@captain_nello]

he probably just uses a pen

[@Naruto0519]

He must have gone to college like 20x with different majors each time to be this damn smart D: That's a lot of money T_T

[@lousyindian]

3:20 Purrramitterrr

[@DearSensational]

"Parameter....." Mahogany...

[@benjamincheung4999]

why are you using t^2/2?

[@COYADD]

How come on my graphing calculator the length of the line ends depending on t? Ex: x(t)=2t The line will only go 2 to the +x direction. But what if t=2? Then x would be 4, but my calculator will only go a certain specified distance.

[@anandar773]

superrr...

[@benv4]

watch video 2 if u didnt understand where he got t = sqrt (10) :P

[@dadinggo]

Thank God Khan doesn't use imperial like my Calc book. I'll never understand smh

[@purplefire5]

lol i have the same problem my teacher goes WAY TOO FAST but honestly the best tutorial for calculus is patrickJMT (his username on youtube) so you just type in the topic or chapter you're in and his name at the end and search, if he has a video on it his name comes up HONESTLY he has absolutely every topic explained with RLLY good examples that he clearly explains, he is the only reason i have an 87 in calc. just try looking him up he rlly helped me

[@Dotachin2]

does anyone know the program he uses to draw the diagrams?

[@qualquan]

Parametric = multi DGN per IGN? For example polar coords

[@Viccor25]

Unless it's, uh...Unless it's, uh...Unless it's, uh...

[@fatimadarling9656]

How is this precalc when it's part of my last sections in Calculus 2?

[@loverofbeats]

amazing! :D

[@fabse64]

Who writes those subtitles? "And I encourage you to watch the [UNINTELLIGIBLE]" I guess it's not Khanacademy, as he probably would have understood his own words? :P