Calculus Word Problem

**kashifzaidi** · October 25th 2009, 01:57 PM

A plane flies horizontally at an altitude of 6 km and passes directly over a tracking telescope on the ground. When the angle of elevation is pie/3, this angle is decreasing at a rate of pie/6 rad/min. How fast is the plane traveling at that time? (Round your answer to two decimal places.)

**skeeter** · October 25th 2009, 02:12 PM

Originally Posted by kashifzaidi

A plane flies horizontally at an altitude of 6 km and passes directly over a tracking telescope on the ground. When the angle of elevation is pie/3, this angle is decreasing at a rate of pie/6 rad/min. How fast is the plane traveling at that time? (Round your answer to two decimal places.)

did you make a sketch ?

let $x$ = horizontal distance the plane travels

$\cot{\theta} = \frac{x}{6}$

take the derivative w/r to time, substitute in your given and calculated values, then determine the value of $\frac{dx}{dt}$

btw, this is pie ...

this is pi ...

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