Related Rates Test: Ladder Against Wall Video
Raw Transcript
Hello. Tom from everystepcalculus.com
Related Rates. These are word problems. Very difficult
even though seemingly simple but
let’s get started. Index eight is calculus one in my program to get to my menu.
That comes with my instructions of course and we’re going to scroll down to
from the menu on a scroll down to related rates. Could be on a test
homework or something and we find it all alphabetical
and in this case
we’re gonna do a ladder against the wall which is the usual
calculus problem related race
problem. It’s used in the Kahn Academy
for their example and also in this example here
from number nineteen. So when I scroll down to that
and we’re going to press enter.
I show you what it looks like. Here’s the ladder
and here of course is the y axis and the x axis. All related rates
are right triangle basically. And they
I ask for them at ladder length. You have to press alpha before you enter anything in
the my entry lines in my programs
and they give it as five meters.
And then you have to decide which is changing.
Is the ladder moving down the y axis
or is the bottom moving? Do they give you the bottom moving right or left?
So, in this case is the y is
the ladder is moving down to give you that change.
So we’re going to choose number two here.
Press Alpha again and they give that to you
as one meters per second so we’re going to choose one. Press enter.
And then they give you
certain distance on the x axis so we’re going to
press and that you need to use three. So we have these
parameters given. I ask you if that’s correct.
You can change it if you want. I say it’s okay.
The first thing with these ladder problems is that you have to find out the other side so
of course x squared plus y squared equals z squared and the
one that we don’t know is the y. We know the x is three and we know the
ladder is 5 so we need to figure that out.
So we do that automatically for you here.
It’s 4 units. I say units because they may be centimeters it, it might give you millimeters, it might give you something else.
You decide yourself and put those in for units.
In this case are getting in meters.
And then they the use implicit differentiation to
to differentiate these
terms here and so we have to do the derivative
of x squared, the derivative of y squared with respect to T
and T is time. The x axis is actually time also.
and z squared. We know z squared is 5 so you write all
this on your paper.
and it turns out to be a -1.33 units per second.
Pretty neat. everystepcalculus.com Go to my site, buy my programs and subscribe
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