Related Rates - The Ladder Problem

This calculus video tutorial explains how to solve the ladder problem in related rates. It explains how to find the rate at which the top of the ladder is sliding down the building and how to find the rate at which the area formed by the ladder is changing. In addition, it explains how to determine the rate at which the angle formed by the ground and the ladder is changing with respect to time using derivatives and implicit differentiation.
Introduction to Limits:
• Calculus 1 - Introduct...
Derivatives - Fast Review:
• Calculus 1 - Derivatives
Introduction to Related Rates:
• Introduction to Relate...
Derivative Notations:
• dy/dx, d/dx, and dy/dt...
Related Rates - The Cube:
• Related Rate Problems ...
__________________________________
Inflated Balloon & Melting Snowball:
• Related Rates - Inflat...
Gravel Dumped Into Conical Tank:
• Related Rates - Gravel...
Related Rates - Area of a Triangle:
• Related Rates - Area o...
Related Rates - The Ladder Problem:
• Related Rates - The La...
Related Rates - The Distance Problem:
• Related Rates - Distan...
____________________________________
Related Rates - Airplane Problems:
• Related Rates - Airpla...
Related Rates - The Shadow Problem:
• Related Rates - The Sh...
Related Rates - The Baseball Diamond Problem:
• Related Rates - The Ba...
Related Rates - The Angle of Elevation Problem:
• Related Rates - Angle ...
Related Rates - More Practice Problems:
• Related Rates - Conica...
_________________________________
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[@TheOrganicChemistryTutor]

Next Video: kzbin.info/www/bejne/laTFommvj55-qpo Final Exams and Video Playlists: www.video-tutor.net/

[@pedrooreosg9180]

looks like im gonna be watching every single related rates video

[@billiamsquilliam]

@@lochtlmao same, 40x better than my professor

[@abuzharrluqman9304]

emm I think he does post an hour video regarding all types of related rates problems

[@insert6190]

Same here

[@Sol-01]

@@billiamsquilliam my professor always seems to confuse the fuck out of everything

[@nickwright2721]

Same

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He really posts this stuff for free... You are my daddy. My super hero.

[@cassied9327]

This was a perfect example question. It touched upon so much good stuff, in a practical and relatable problem.

[@theobserver314]

Relatable. I see what you did there.

[@briantaylor512]

I just want to thank you for helping me in each of my math classes. Your videos are an invaluable resource, looking forward to being a paid subscriber soon!

[@Undertakerfan700]

We had a similar problem in class like this. It’s way more clear now. Thank you!

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these have helped me so much, both your videos on physics and calc are amazing!! thank you!!

[@Adiam.Tekle.]

Your videos are so helpful. Thank you!

[@josiahchang5440]

He doesn't even say like and subscribe respect Oh yeah yeah

[@argoneus21]

wow. impressive! 2 hour lecture compressed into clear explanation of 1 problem.

[@georgesadler7830]

MR. Organic Chemistry Tutor, thank you for an outstanding video/lecture on the Ladder Problem in Calculus One. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

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Thank you very much. As always you make it easy.

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this was so helpful thank you!!

[@alexisconcepion1713]

It helped me a lot. Thank you

[@imperiusss]

are you one day going to also teach statistics,cosmology,modern physics? thank you very much for this videos already!!!

[@Noper812]

my man coming in clutch once again

[@Jmnb083]

Thanks for the help 😄

[@coreygraham1160]

Literally used this to do my signature assignment in 13 minutes thank the maker

[@loldawg7518]

thank you so much perfect example

[@TheFarmanimalfriend]

The right triangle can be used to establish dy/dt. Ladder length is constant. Because of it we know y = 9 feet and we know dy/dt is negative (y is losing height, 8 ft). We also know -dy/dt = dx/dt and we know when y = 9, dy/dt = -16.00 feet/sec, so dx/dt = 16.00 feet/sec. gravity = 32 feet/sec^2 or 9.8 meter/sec^2

[@earlsayam3823]

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[@dr.alnaqbi7745]

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Thanks Kang

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[@MrRgl12]

everyone in the comments saying thanks make sure yall like the vid! 78k views and not even 1k likes...

[@taki4707]

Theres only 50 comments

[@kurooackerman7338]

thank you so much

[@smozef]

For letter b, can I ask why the constant 1/2 was included when the derivative of the right side was taken? Aren't constants taken out before taking the derivative of the variables? TIA

[@SierNotsruht]

Probably just a personal idiosyncracy because it shouldn't change the answer

[@tracyvtv]

At 3:35 , isn't 8 and 15 a constant as well? But we still took the derivative like normal, unlike Z, which became 0

[@Anonymous51701]

Tracy Vu The length of the ladder will ALWAYS be 17. However, with Y and X, their distance will change relative to the ground, which means that they CAN CHANGE. Hope this helps!

[@chandana3883]

@@Anonymous51701 thank you

[@Aryan-qt6pu]

the height and length (x and y) CAN change.

[@The541killer]

this guy makes math sound easy

[@djralphzkieeofficial6064]

A 10-foot ladder is standing vertically against the side of a house. The base of the ladder is pulled away from the side of the house at the rate of 1 foot per second. How fast will the top of the ladder by falling down the side of the house 9 second after the base begins being pulled away from the house?

[@thegracegong]

The best!

[@jameswallace9906]

How do you know all this stuff I watch these vids for all my subjects I mean Your like the font of knowledge

[@spacxe2021]

thanks man

[@johnnolen8338]

@ 10:39 "I'm gonna use sin θ." Sin θ involves value(s) that you had to calculate; whereas cos θ involves only given information. Therefore recommend using cos θ because there's less opportunity for error.

[@superepiic]

but you need to calculate the derivative of sinθ, so it would be using cosθ. doing the derivative of cosθ would be -sinθ which is more work and opportunity for error

[@johnnolen8338]

@@superepiic No, sine or cosine is not the issue. The issue is that d sin θ/dt is related to dy/dt (a calculated value); whereas, d cos θ/dt is related to dx/dt (a given value). It makes no difference if you use sine or cosine in practical terms bcz the triangle is a Pythagorean triple: 8, 15, 17. With that fact in hand, it is unlikely that you will make error calculating either ratio.

[@superepiic]

@@johnnolen8338 You're right. But in other problems though, it would depend

[@johnnolen8338]

@@superepiic I agree. It always depends. In this case the rates you want to relate are dθ/dt and dx/dt, which makes cosine the obvious choice in my opinion; but hey, do whatever works for you. 🤙

[@danielfrt]

Why the speed of the sliding ladder on the foot is different from the one in the top?

[@eggxecution]

excellent

[@sm__akash]

How to find the velocity of top of the ladder at time t ??

[@zzzzZZZZzzzz305]

I REALLY HATE THIS KIND OF PROBLEM THANK YOU BEST TEACHER

[@omaryehya8594]

my English professor was so bad at explaining this thanks man.

[@ignantxxxninja]

at 8:31 how does the units of measurement change from ft/sec to ft^2/sec...

[@ignantxxxninja]

oh ok because we're multiplying ft by ft/sec got it

[@Anthony-dy2cv]

So for part c, why did he start with sin theta instead of cos theta??

[@yarielhernandez929]

8:23 wouldn't dA/dt be (-161/10) since the area of the triangle is getting smaller as the ladder slides away from the wall and down it simultaneously?

[@geenarustia354]

Does it matter which one I would label x,y,z ? For first problem. Thank you

[@SierNotsruht]

No

[@zubair1424]

Can someone please explain how at 5:36 the derivative of A is da/dt and the derivative of Z was 0 and not dz/dt. I am deffinately missing something fundamentally, can you point me which video to watch understand the concept better?I thought derivatives of variables were 0 and constant were dvariable/dt

[@pickolzi5312]

Sorry for being late but for anyone else who needs it. A is a variable and it is changing(isn't a constant) so you can find the derivative of it as (dA/dt). The derivative of Z is 0 because Z IS A constant, Z never changes unlike x, y, or A, and the derivative of a constant is 0.

[@Singh-Playz]

@@pickolzi5312 thank u broddie

[@SierNotsruht]

Z is a constant

[@parkercampellone8276]

for anyone else, I feel like it still wasn't explained in a way that is truly understandable. You cannot take the derivative of z, because z is representing the length of the ladder. unlike x, y, and a that all change as the ladder moves, no matter where the ladder moves, the ladders length (z) does not change. a 17 foot ladder is still going to be a 17 foot ladder at any value of x,y, or a.

[@divinest]

i hope this doesn't come out in my test

[@cassied9327]

Divinest Beats I know the feeling. This is one I hope does come up because miraculously I get this one. The ones about spheres (usually balloon volume and radius) or are the ones I’m scared for.

[@Theojoe190]

Better than my lecturer

[@btsmochimi7924]

how do you know if we should be using sine or cosine for getting the angle

[@SierNotsruht]

Its situational

[@whymyruffles]

gosh im falling in love with calculus ngl

[@SierNotsruht]

Calculus is very enjoyable

[@DonClavaton]

Can somebody tell me why the cos pi/3= 1/2

[@gayekaya1655]

could we calculate de a part from area formula (x*y)/2

[@SierNotsruht]

Yes, its the same

[@milnews3933]

In part c, why didn't you derive the 1/z?

[@craigeeyt2826]

the foot of the ladder leaning against the wall is 6ft away from the wall and its top is 8ft above the ground. what is the length of the ladder? A.4ft B.12ft C.16ft D.100ft E.5ft What is the correct answer?

[@niki-mendozacatalan5903]

okay why is Z 0? should its derivative would be 2z(dz/dt) like x and y ??? Im so confuse!! HELP!!

[@MrCreepermax16]

He explained why, z is a constant given to you in the problem. Therefore because its a constant the derivative of it will be zero

[@niki-mendozacatalan5903]

RojekJ but how do you differentiate constant to a variable if all x y and z have values

[@MrCreepermax16]

@@niki-mendozacatalan5903 Z is constant because the length of the ladder never changes. The x value will be changing because the ladder will be sliding away from the wall, if that makes any sense. you have to solve for Y so its not a constant. Im a calc student at the moment, so I am by no means an expert, this is just my take on the problem. Hope this helps

[@niki-mendozacatalan5903]

RojekJ oh yehhh! That make sense now thank you, i completely ignored what Z represent. I better right things down when I illustrate this type of problem. ☺️

[@itssheeza2324]

Why can't I do this looking at it for the first time? Is it because I don't have enough background knowledge? I'm a a generally intelligent student and I'm tired of calc rn I'm not getting probs instantly unlike other students?? Can someone give me a cure?

[@ajsolis2910]

Sheeza Saleem Practice is the way

[@peterveneussvelasco9867]

Why is the unit for d theta over dt is rad/sec???

[@MR.SVR101]

Because the unit of Theta is rad per second

[@ifunny1343]

What if the y is given and the base”x” is not?

[@SierNotsruht]

Same method

[@CarExhaustEater]

this is such a cool video! *brap* hahahahaah sorry I'm kind of gassy today

[@niki-mendozacatalan5903]

why did you use sin instead of cos? you need to explain it please

[@jiachen8353]

it is the same thing. but just avoid tangent for this problem in particular coz there are 2 variables. cos and sin no matter which one are okay.

[@fbvmivfma5237]

arent x and y also constants not just z

[@EhlekCoolDude]

no as the values of x and y are changing as the ladder moves y is getting smaller and x is getting bigger

[@beknurziyabek90]

why z is constant? if so why x or y are not constant?

[@alexan406]

z is constant because it is the length of the ladder. On the other hand, x, represents the distance of the foot of the ladder to the wall and y represents the height of the top of the ladder. Therefore, x and y are always changing meaning they are not constant.

[@wummrs]

How come Z is considered a constant but not x and y???

[@murdock5537]

because the ladder has a length of 17 feet - (it's fixed :-)

[@Nocturtle117]

I love you

[@Maryiah_]

First year:2nd sem final exam attendance check I hope I can graduate on time on my program BSECE

[@lyndonkylelagpacan2631]

Probably a dumb question, but why would Z be a constant and X and Y are not? Edit: nvm I should’ve watched the whole thing first

[@IBtehOmar]

because z is the height of the ladder so it doesnt change

[@thomasmcgrath6023]

buildin

[@scattered9brain]

I love u

[@pistapola642]

WHAT IF IM FINDING THE dx/dt huHU HELP

[@user-sm4lm5fq2t]

i disagree with z squared derivative being a zero because its a number then y should aslo have been zero since its 8 n y too

[@cloroxbleach4219]

that's because x is 8 at that specific moment but z is always 17 as the length of the ladder doesnt change

[@HealersRoots5thSeed]

comment for the algorithm :D

[@unotacothesecond4114]

🐐🐐🐐

[@heranh9440]

I can't express by word sir

[@heranh9440]

God bless you

[@shellysdopevids6988]

I hate related rates

[@ghaidakhiami]

i owe u my diploma

[@brysonbrown92]

part A wouldn't be negative because it's not sliding down the wall at negative ft/s. it's just sliding down the wall at ft/s. no such thing as negative velocity

[@Anonymous51701]

Velocity is a vector. The negative simply implies that the object is moving on the opposite side. (For example, left). Negatives do exist in velocity. Only in speed, you cannot have negatives (because its scalar)

[@SierNotsruht]

Sure but the coordinate is decreasing so its justified

[@kezriehayudini9137]

3:24 you lost me here.

[@christinagomez]

I got confused at the same spot, then realized that the size of the ladder does not change. Hopefully you figured this out a year ago too.

[@peacepath4350]

Subtitles are hiding the written stuff

[@ezabellakhan8488]

i am so deeply in love wit u

[@calvinbenson2796]

have my children

[@Et_sapien]

Bro solved every problem except global warming

[@TheFarmanimalfriend]

You cannot ignore the acceleration due to gravity. Students who need help will only get confused. Units attached to the variables are critical. You cannot add and subtract variables with different units, but you can multiply, divide and apply exponents to these variables and their units with the same operation. Please help students - don't confuse them

[@engr.rimarc.liguan1795]

Time rates is for Calculus is just mathematical representation of variable equations. Its an application of the rate of change neglecting the effects of referential frames. And always assumes constant change. If it was introduced to Physics, then it could have an additional effects from the referential frame, eg. Gravity, air resistance, mass/weight, force (pull or push) and other contributors.