Thread: Drone Aeroplane distance changing at an instant

A drone aeroplane is flying horizontally at a constant height of 4000 ft above a fixed radar tracking station. At a certain instant the angle of elevation theta is 30 degrees and is decreasing, and the speed of the drone aeroplane is 300 mi/h. How fast is the distance between the aeroplane and the radar station changing at this instant? Express the rate in units of ft/s. Use 1 mi=5280 ft

Originally Posted by titansfreak93

A drone aeroplane is flying horizontally at a constant height of 4000 ft above a fixed radar tracking station. At a certain instant the angle of elevation theta is 30 degrees and is decreasing, and the speed of the drone aeroplane is 300 mi/h. How fast is the distance between the aeroplane and the radar station changing at this instant? Express the rate in units of ft/s. Use 1 mi=5280 ft

sketch a diagram?

let = straight-line distance between radar site and drone

let = horizontal distance between radar site and drone

let = plane's altitude (note that the altitude is in feet)

note when , and





take the time derivative of the above equation, substitute in your known (and calculated) values, and determine

pay attention to units