A plane that flies horizontally at an altitude of 19mi and a speed of 90 mi/hr passes directly over a tracking telescope on the ground. if the telescope is always aimed at the plane, how fast is the telescope's angle of elevation decreasing after two hours? round your answer to two decimal points.
Make a sketch of the situation.
At a time of t hours let the horizontal distance of the plane from
the tracking station be x miles
let the angle to the plane be θ radians
tan θ = 19/x
xtanθ = 19
xsec^ θ dθ/dt + tanθ dx/dt = 0
when t = 2, x = 180,
tanθ = 19/2
sec^2 θ = 365/4
xsec^ θ dθ/dt + tanθ dx/dt = 0
180(365/4) dθ/dt + 19/2 (90) = 0
16425 dθ/dt = - 855
dθ/dt = -.052 rad/hr