Related Rates TI-89: Airplanes in Flight
Related Rates Test Question: Two airplanes pass each other in flight at 9:00 AM.
One is traveling East at 90 mi/h. The other is traveling South at 180 mi/h. How fast are they
separating at 11:00 AM?
Hello Tom from every step calculus dot com.
Going to do related rates problem. Let’s get started.
index8() in the entry line here to get to my menu.
Press Enter. We need
related rates are we could get average average rate of change.
Both the same.
And we’re gonna do in this problem this is two airplanes passing each other.
At a certain time. And
what’s their rate of change as they separate. And
in these kind of problems we’re gonna, we’re gonna go to north, south, east or west.
In the menu which is number 8.
You can scroll down with the curser or you can press the number before it.
I press number. And
were going to do the problem. The most important part of north and south
is this pathagorum theorem type thing which is,
and then the derivatives of that. Your
both sides of the equation to come up with the most important part. Here’s the
thing if you can figure out
(x) and dx/dt.
(y) and dy/dt and your gonna get
dz/dt which is most the time what they ask for.
Which is the hypotenuse of a right triangle.
So make sure you mark this down on your paper.
Here’s how you got it.
Of course the 2’s are cancelled, I put this here.
They always give you time. So in this,
in this problem they give 9:00 am so we’re gonna press number two to go to a.
And we’re going to push alpha, to push
alpha before you enter anything in these entry lines here.
alpha 9 a.m. and the other one is
a.m. also so I’m going to press to 2 here. And put in alpha
11. I will show you what you’ve
entered, so you can change it if it’s a mistake, 9 AM and 11.
And of course that’s two hours elapsed time
in between this flight here. And we’re going to enter the speed of the
first plane which is
Miles per hour we’re going to choose number 3. And the direction here is East. We’re going
to choose number three again.
And then we have the other plane which is
And that’s going south, we’ll press number 4.
The miles per hour will be the same for both. It will be the same.
So here again I show you’ve entered you can change it if you want.
I say it’s okay. And
the first thing you do is find out X with respect to time.
So about 90 miles per hour.
And about two hours it’s 180 miles per hour.
You write this down on your paper, there’s a system for doing these problems.
on related rates. Then we need to know the hypotenuse
that’s the pathagorum theorem. So we do it here, you write this on your paper
that’s 402 miles per hour, that’s the hypotenuse.
And you plug these factors in X 180 dx/dt
was 90 and here’s 360.
And dy/dt was 180, divided by 402
which is, and this is the formula here.
(x) dx/dt plus y dy/dt
divided by z equals dz/dt which is they’re asking for. So 201
miles per hour. 100 percent on this problem on
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