Derivative word problems

• Mar 15th 2012, 11:01 AM
NotAMathmatician314
Derivative word problems
The problem is as follows:

An airplane flies at an altitude of 5 miles towards a point directly over an observer on the ground. The speed of the plane is 600 miles per hour. Find the rate at which the angle of elevation "theta" is changing when the angle is theta=pi/6 (approximate to four decimal places.)
• Mar 15th 2012, 12:22 PM
skeeter
Re: Derivative word problems
Quote:

Originally Posted by NotAMathmatician314
The problem is as follows:

An airplane flies at an altitude of 5 miles towards a point directly over an observer on the ground. The speed of the plane is 600 miles per hour. Find the rate at which the angle of elevation "theta" is changing when the angle is theta=pi/6 (approximate to four decimal places.)

let x = the horizontal distance the plane is from the observer

$\frac{dx}{dt} = -600$ mph

$\tan{\theta} = \frac{5}{x}$

take the time derivative of the above equation, sub in your known values and determine the value of $\frac{d\theta}{dt}$ when $\theta = \frac{\pi}{6}$