An airplane is flying at a constant speed and altitude on a

An airplane is flying at a constant speed and altitude, on a line that will take it directly over a radar station located on the ground. At the instant when the airplane is 60,000 feet from the station, an observer in the station notes that its angle of elevation is 30 degrees and is increasing at the rate of 0.5 degrees per second. Find the speed of the airplane.

Solution

cos() = x / 60000
-sin() d/dt = 1/60000 dx/dt
-sin(/6) (/360) = 1/60000 dx/dt

1/2 deg/s = /360 radians/s
dx/dt = -250/3 ft/s = -625/11 mph

625/11 mph 178.5 mph