What is the speed of the airplane?

Question

An airplane flying at an altitude of 6 miles passes directly over a radar antenna (see figure). When the airplane is 10 miles away (s = 10), the radar detects that the distance s is changing at a rate of 240 miles per hour. What is the speed of the airplane?

Answer 1

From the diagram, 6² + x² = s² Then, 2xdx =2sds So, 2x dx/dt = 2s ds/dt

when s = 10 x = sqrt( 100-36) = 8

or plane speed = dx/dt = (s/x) ds/dt substituting we have dx/dt = (10/8)(240) = 300 mph