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!
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
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 TH-cam TV with the Organic Chemistry Tutor.
@ 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.
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
@@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 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. 🤙
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!
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
Nice explanation Love it Like it as well Keep going on Impressive work Btw anyone wondered about this guy name because this guy came from a genius planet :)
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?
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?
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.
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
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.
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.
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?
@@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
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. ☺️
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.
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
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)
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
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.
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looks like im gonna be watching every single related rates video
@@lochtlmao same, 40x better than my professor
emm I think he does post an hour video regarding all types of related rates problems
Same here
@@squilleam my professor always seems to confuse the fuck out of everything
Same
He really posts this stuff for free...
You are my daddy. My super hero.
This was a perfect example question. It touched upon so much good stuff, in a practical and relatable problem.
Relatable.
I see what you did there.
We had a similar problem in class like this. It’s way more clear now. Thank you!
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!
these have helped me so much, both your videos on physics and calc are amazing!! thank you!!
He doesn't even say like and subscribe respect
Oh yeah yeah
wow. impressive! 2 hour lecture compressed into clear explanation of 1 problem.
my man coming in clutch once again
Literally used this to do my signature assignment in 13 minutes thank the maker
if no one got me i know the organic chemistry tutor got me
are you one day going to also teach statistics,cosmology,modern physics? thank you very much for this videos already!!!
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
This man is goated, he has helped me pass so many test and quizzes
Your videos are so helpful. Thank you!
everyone in the comments saying thanks make sure yall like the vid! 78k views and not even 1k likes...
Theres only 50 comments
Your videos are really helpful Thanks
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 TH-cam TV with the Organic Chemistry Tutor.
@ 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.
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
@@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.
@@johnnolen8338 You're right. But in other problems though, it would depend
@@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. 🤙
this guy makes math sound easy
Bro got me through High School and now Uni lol
Legend
How do you know all this stuff
I watch these vids for all my subjects
I mean
Your like the font of knowledge
It helped me a lot. Thank you
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
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!
@@Anonymous51701 thank you
the height and length (x and y) CAN change.
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
Probably just a personal idiosyncracy because it shouldn't change the answer
I REALLY HATE THIS KIND OF PROBLEM
THANK YOU BEST TEACHER
this was so helpful thank you!!
Nice explanation
Love it
Like it as well
Keep going on
Impressive work
Btw anyone wondered about this guy name because this guy came from a genius planet :)
my English professor was so bad at explaining this thanks man.
Thank you very much. As always you make it easy.
thank you so much perfect example
Thanks Kang
gosh im falling in love with calculus ngl
Calculus is very enjoyable
Better than my lecturer
Thanks for the help 😄
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?
Thank you 🙌
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?
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
because z is the height of the ladder so it doesnt change
The best!
excellent
God bless you
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?
i hope this doesn't come out in my test
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.
thanks man
thank you so much
how do you know if we should be using sine or cosine for getting the angle
Its situational
this is such a cool video! *brap* hahahahaah sorry I'm kind of gassy today
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
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.
@@pickolzi5312 thank u broddie
Z is a constant
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.
Does it matter which one I would label x,y,z ? For first problem. Thank you
No
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?
Sheeza Saleem Practice is the way
In part c, why didn't you derive the 1/z?
So for part c, why did he start with sin theta instead of cos theta??
Why the speed of the sliding ladder on the foot is different from the one in the top?
okay why is Z 0? should its derivative would be 2z(dz/dt) like x and y ??? Im so confuse!! HELP!!
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
RojekJ but how do you differentiate constant to a variable if all x y and z have values
@@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
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. ☺️
How to find the velocity of top of the ladder at time t ??
arent x and y also constants not just z
no as the values of x and y are changing as the ladder moves y is getting smaller and x is getting bigger
First year:2nd sem final exam attendance check
I hope I can graduate on time on my program BSECE
why did you use sin instead of cos? you need to explain it please
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.
could we calculate de a part from area formula (x*y)/2
Yes, its the same
What if the y is given and the base”x” is not?
Same method
why z is constant? if so why x or y are not constant?
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.
How come Z is considered a constant but not x and y???
because the ladder has a length of 17 feet - (it's fixed :-)
Can somebody tell me why the cos pi/3= 1/2
Why is the unit for d theta over dt is rad/sec???
Because the unit of Theta is rad per second
comment for the algorithm :D
I love you
3.7
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
that's because x is 8 at that specific moment but z is always 17 as the length of the ladder doesnt change
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
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)
Sure but the coordinate is decreasing so its justified
buildin
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WHAT IF IM FINDING THE dx/dt huHU HELP
I can't express by word sir
God bless you
Subtitles are hiding the written stuff
I hate related rates
3:24 you lost me here.
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.
Bro solved every problem except global warming
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
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.
i am so deeply in love wit u
have my children
at 8:31 how does the units of measurement change from ft/sec to ft^2/sec...
oh ok because we're multiplying ft by ft/sec got it