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/4, this angle is decreasing at a rate of π/4 rad/min. How fast is the plane traveling at that time? (Round your answer to two decimal places.)
2 answers
That looks hard
Draw a diagram. If the plane's horizontal distance is x,miles, then
tanθ = 5/x
sec^2θ dθ/dt = -5/x^2 dx/dt
So plug in your numbers and find dx/dt
tanθ = 5/x
sec^2θ dθ/dt = -5/x^2 dx/dt
So plug in your numbers and find dx/dt
4 answers