# Related rates problem

• Nov 5th 2012, 12:08 PM
PhizKid
Related rates problem
A plane flies horizontally at an altitude of 5 km and passes directly over a tracking telescope on the ground. When the angle of elevation is is pi/3, this angle is decreasing at a rate of pi/6 rad/min. How fast is the plane travelling at that time?

http://i.imgur.com/mbKzq.png

Now I need to find 'y' which is impossible because I only have one given side and one angle. How do I solve the rest?
• Nov 5th 2012, 12:10 PM
PhizKid
Re: Related rates problem
Also I forgot to add in the Chain Rule for the differentiation, so there should be a dtheta/dt added onto that second term. But we already know that value so the problem is still finding the y.
• Nov 5th 2012, 12:27 PM
skeeter
Re: Related rates problem
$\cot{\theta} = \frac{y}{5}$

$-\csc^2{\theta} \cdot \frac{d\theta}{dt} = \frac{1}{5} \cdot \frac{dy}{dt}$

$-5\csc^2{\theta} \cdot \frac{d\theta}{dt} = \frac{dy}{dt}$

plug and chug the left side and evaluate $\frac{dy}{dt}$