An airplane flies at an altitude of y = 8 miles toward a point directly over an observer (see figure).

Question

An airplane flies at an altitude of y = 8 miles toward a point directly over an observer (see figure). The speed of the plane is 600 miles per hour. Find the rates at which the angle of elevation 𝜃 is changing when the angle is 

a)𝜃 = 45°, rad/min

 b)𝜃 = 60°, rad/min

 c) 𝜃 = 80°. rad/min  (Round your answer to two decimal places.)

Answer 1

The horizontal distance from the plane to the observer is x

and x/8=tan θ.

dx/dt = 600 = 8 sec²θ dθ/dt dθ/dt= 75 cos²θ

Now plug in the angles requested.

I made an error in the angle I called θ.

As a result the answer should have been θ:x/8=cot θ

dx/dt = 600 = -8csc²θ dθ/dt = 75 sin²θ

and yes, plug the angle values into this last equation.

Answer 2

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