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Title: Calculus problem:
Post by: Moonshine on March 04, 2004, 01:40 AM

I was bored, and I saw this problem on another forum. Let's see if any of you people can get this one :)

A plane flies over a radar tower six miles above the ground. The distance between the plane and base of the tower is increasing at a rate of 400 mph. When the plane is ten miles out from the tower, at what speed is the plane traveling?

V=?

Title: Re:Calculus problem:
Post by: Adron on March 04, 2004, 03:30 AM

Quick semi-formal calculation...

Code Select




                        b=10mi
            >---->---->---->---->----> plane
            |                    ----
            |                ----
       a=6mi|            ----
            |       ----  c
            |   ----
            +---
            Tower




c = sqrt(a^2 + b^2) = sqrt(10^2 + 6^2)

b = (c^2 - a^2)^0.5

a' = da/dt = 0
c' = dc/dt = 400 mph

b' = db/dt = c'*2*c*0.5*(c^2 - a^2)^-0.5 = c' * c/b = 400 * sqrt(136)/10 ~= 466 mph

Does it look right?

edit: edited values that i'd misread

Title: Re:Calculus problem:
Post by: j0k3r on March 04, 2004, 05:57 AM

400mph?

Title: Re:Calculus problem:
Post by: jigsaw on March 04, 2004, 06:19 PM

You dont *need* calculus to do that. Just makes life easier. Btw this belongs in Yoni's math forum :)

Title: Re:Calculus problem:
Post by: Adron on March 04, 2004, 07:22 PM

Oh, oops. Well, insert the right value into the formula, and then see if it looks right? :P

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General => General Discussion => Topic started by: Moonshine on March 04, 2004, 01:40 AM