Another differentiation word problem

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Stealmylilhart

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Oct 31, 2006
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An air traffic controller spots two planes at the same altitude converging on a point as they fly at right angles to each other. ONe plane is 150 miles from the point moving at 450 miles/hour. The other plain is 200 miles from teh point movine 600 miles/hour.

a. At what rate is the sitance between the planes decreasing.

b. How much times does the air traffic controller have to get one of the plaines on a different path.
 
No one got as much as a 'thx' on the last post so someone may help...they may not.

Which direction are the planes flying, respectively?.

This appears to be similar to the last problem. Think Pythagoras.
 
Mostly I would just like to know how to do the second part do I just use the D = RT....formula...I think I got the first part...do I have to differentiate the D = RT formula?
 
Thanks for the thanks.

Assuming this is the right directions of the planes.

When you see a problem like this, remember Pythagoras.

planesxn8.gif


\(\displaystyle \L\\D^{2}=x^{2}+y^{2}\)

Differentiate:

\(\displaystyle \L\\2D\frac{dD}{dt}=2x\frac{dx}{dt}+2y\frac{dy}{dt}\)

Use Pythagoras to find D when x=200 and y=150

Enter in your data and solve for \(\displaystyle \frac{dD}{dt}\)

Remember negatives where they belong.
 
Thanks so much, ya I think that is what I did....in the second part of the question can I just use the info for one plane to determine the time? :D
 
Yes, just plug in your info and solve for dD/dt

Use Pythagoras to find D= \(\displaystyle \sqrt{150^{2}+200^{2}}\)

dx/dt=600, dy/dt=450, x=200, y=150

Remember, use negatives where appropriate. This is assuming my diagram is correct. You did not list directions of the planes.
 
the one plane at 150 m/h is going down(south), while the second plane is going left(west)....
[/img]
 
Stealmylilhart said:
the one plane at 150 m/h is going down(south), while the second plane is going left(west)....
Click to expand...
Okay.... So what have you done? You've had very similar exercises worked out for you. What progress have you made in learning and working from these solutions?

Please be specific. Thank you.

Eliz.
 
I think that I have it fine...my main issue with these problems is setting them up and deciding on the write equation to use, because we do a lot of different area ones, etc. I can differentiate fine, i have no issues with that. Im just trying to practice on setting these up. Thanks for the help though. What you guys are writing is helping me to understand what I need to think about for setting them up. :oops:
 
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