Question

A drone aeroplane is flying horizontally to 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 decreasing, and the speed of the aeroplane is 300 mi/h

a) How fast is theta decreasing at this instant? express results in units of deg/s

b) How fast is the distance between the aeroplane and the radar station changing at this instant? express the rates in units of ft/s 1 mi = 5280ft

Answer 1

If I get the picture accurately

a) height/horizontaldistance away= sinTheta

height= distancaway*sinTheta
take the deriviative
0=d (distance)/dt *sinTheta- distance*cosTheta dTheta/dt

well d (distance)/dt=velocity= 300mi/hr

dTheta/dt= tanTheta*300mi/hr / distance

but distance= height/sin30 then solve for dTheta/dt. Change mi/hr to feet/sec (ie 60mph=88ft/second)