Question

A plane flying horizontally at an altitude of 2 mi and a speed of 470 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 6 mi away from the station.

Answer 1

6 mi horizontally away ?

Answer 2

yes from the station

Answer 3

draw a triangle. one leg is 2, but the other leg x (that is the horizontal distance) and the hypotenuse is Y. that being the distance from the plane to the station

Answer 4

i should say a "right triangle"

Answer 5

pythagoras tells you
\[2^2+x^2=y^2\] you know
\[\frac{dx}{dt} = 470\] because that is what you were given. you want
\[\frac{dy}{dt}\]

Answer 6

take the derivative of the pythagorean identity wrt t and get
\[2x\frac{dx}{dt}=2y\frac{dy}{dt}\]or
\[\frac{dy}{dt}=\frac{x}{y}\frac{dx}{dt}\]

Answer 7

plug in the numbers and you are done. you know
\[\frac{dx}[dt}=470, y = 6 and find x by pythag

Answer 8

\[\frac{dx}{dt}=470, y = 6 \]

Answer 9

ok thanks!!!