An Airplane is flying at an elevation of 6 miles on a flight path that will take it directly over a radar tracking station. If the distance between the plane and the station is decreasing at a rate of 400 mph when the plane is 8 miles away from being directly over the station, what is the speed of the plane?

Question

An Airplane is flying at an elevation of 6 miles on a flight path that will take it directly over a radar tracking station.  If the distance between the plane and the station is decreasing at a rate of 400 mph when the plane is 8 miles away from being directly over the station, what is the speed of the plane?

oobleck · Accepted Answer

when the plane is x miles away from overhead, we have the distance z is z^2 = 6^2 + x^2 z dz/dt = x dx/dt so at the given moment, z=10, so 10(-400) = 8 dx/dt dx/dt = -500 mi/hr