Calculus problem:

[Moonshine]

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=?          

[Adron]

Quick semi-formal calculation...

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                       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

[j0k3r]

400mph?

[jigsaw]

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

[Adron]

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