A plane flying horizontally at an altitude of $1 \mathrm { mi }$ and a speed of $550 \mathrm { mi } / \mathrm { h }$ passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is $2 \mathrm { mi }$ away from the station.
A) $\approx 476 \mathrm { mi } / \mathrm { h }$
B) $\approx 670 \mathrm { mi } / \mathrm { h }$
C) $\approx 455 \mathrm { mi } / \mathrm { h }$
D) $\approx 570 \mathrm { mi } / \mathrm { h }$
E) $\approx 495 \mathrm { mih }$

Question

Quizplus · Accepted Answer

Using the Pythagorean theorem, the distance from the plane to the station is $ \sqrt{x^2 + 1^2} $. Differentiating with respect to time and substituting $ x = \sqrt{3} $ (since $ \sqrt{3^2 + 1^2} = 2 $) and $ \frac{dx}{dt} = 550 $, we find the rate is approximately $ 476 \mathrm{ mi } / \mathrm{ h } $.

A Plane Flying Horizontally at an Altitude Of 1mi1 \mathrm { mi }1mi

A Plane Flying Horizontally at an Altitude Of $1 \mathrm { mi }$