An airplane is cruising at 340 km/h at an altitude of 4000 m. If the plane passes directly over an observer on the ground, how fast is the distance from the plane to the observer changing when it is 3000 m away from the point directly above the observer?

Answer 1

if the distance from the plane to the observer is y, and the distance the plane has flown is x, all in km,

y^2 = 4^2 + x^2
2y dy/dt = 2x dx/dt
when x = 3, y=5
10 dy/dt = 2(3)(340)
dy/dt = 204 km/hr