Related rates: Falling ladder | Applications of derivatives | AP Calculus AB | Khan Academy

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You're on a ladder. The bottom of the ladder starts slipping away from the wall. Amidst your fright, you realize this would make a great related rates problem... Created by Sal Khan.

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

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This guy is good at math, maybe he should be a teacher or something.

Anaghish
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this is way easier than my professor made it seem

bcnicholas
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Your drawings make me feel emotions ive never felt before :, )

elliot
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That ladder cartoon is intense, oh and good math and such

sincostanlogin
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Thanks for this video, I had been messing around for ages and you explained it in seconds!

jessemaretzki
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That was an amazing lesson.  I've gone through so many videos and they skip steps because they do them in their head, but I like to know why and how to everything.  Thanks for posting something that makes sense and is in clear English.

lauracantu
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practice simple area equations, cones, cylinders, triangles. . . THANKS, this one wasnt bad :D

tasadar
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color makes it easier to understand what those numbers signifies

vandammeangelo
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this is great.calculus word problems. please do more

homousios
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I wonder why people chose to invent this.

TheManMeta
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your videos are amazing! you make it so easy to understand. thank you so much khan!!!! & keep up the great work (:

tddybars
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this would work only if the height decreased linearly, but it does not because the two shorter sides of a right triangle are connected by the tan function (height = the tan function is not linear, so the height does not decrease linearly as distance from wall increases, rather it decreases at different rates at different points in time.

killie
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Right before the ladder, h--> 0, thus dh/dt --> infinity. Fast ladder!

haakonvt
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use the metric system.
Makes a million times more sense.

Mrissecool
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Great Video, I am a bit stuck on a similar problem though. If the ladder is 19 feet long and 3 feet from the wall, how fast will it be falling in the y-direction after one second if it is slipping in the x direction at 1ft/s. Would really appreciate some help on this because I keep getting it wrong. Thanks

MikeGecawicz
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Gravity must be taken into account! The ladder falls because it is being accelerated downwards at 32 feet/sec^2.

TheFarmanimalfriend
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xactly and this is what i used to calculate the speed too. since t=0.5 for ladder to reach floor completely.... at this point the height is = 0. So speed = d/t = 6/0.5 = 12 ft/sec Someone pls explain why this is wrong???

vijeth
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In a way, yes, over complicated. A mathematical model is never perfect. In engineering and physics friction is often treated as a constant, but surface roughness is never a constant and as a result, friction is truly never constant. In most of human ability to measure forces though, we can't tell on a day-to-day event (like a ladder) that friction isn't constant. Point to be made is that there are always improvements to be made to any math model, but we shoot for close enough. :-)

MetPhD
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were did khan get the dx/dt or is it usually given?

kyletanasas
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you forgot to calculate the friction

the friction changes over time as it's different angle

psihokiller