Calculus word problem help

Question

A drone plane moving at 70m/s, flies horizontally at an altitude of 400 meters directly over a radar station. Let 'O' be the angle of elevation of the drone. What is the rate of change of the angle of elevation dO/dx when the drone is x=500m past th radar station. 

Answer 1

tan (O) = 400/x

when x=500 the hyp of the triangle formed is Sqrt(400*2+500*2)=640.312

 

Taking derivative of the equation

sec²(0) dO/dx = -400/x²           sec²(0)= 640.312/500 = 1.13

 

d(O)/dx = (-400/500² )/1.13 = -0.0014

So, the angle of elevation is decreasing at the rate of .0014 radians/sec