I can do related rates problems a little bit, but I've been given one that requires me to use a rate of $\frac{-\pi}{6}$ radians per second to figure out how fast a plane is going. Since I assume that plane is moving in a straight line, I'm not sure how to proceed.
I think the answer might be to find out how fast the given rate is moving in terms of horizontal speed, and then apply implicit differentiation on that to find the answer, but I'm not sure.
I could use the angular velocity formula, $\omega = \frac{\theta}{t}$, but I'm worried that's not the right way since it gives an average.
How can I convert a rate with radians to a rate involving purely horizontal/straight movement?
Problem Text:
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 π/3, this angle is decreasing at the rate of π/6 radians per minute. How fast is the plane traveling at that time?
I have worked through it, and I've discovered that the plane, the telescope, and the distance of the plane from the ground can be formed into a right triangle. Since, $\frac{\pi}{3}$ radians is $60^\circ$ and a right triangle has a $90^\circ$ corner too, that means the the last corner must also be $60^\circ$.
Using the Law of Sines, I have found the hypotenuse is $\frac{10\sqrt{3}}{3}$ kilometers long and the other two edges are both $5$ kilometers.
I haven't been able to get further than that.