A UFO is at one kilometer altitude, and one kilometer due east of a power plant on the ground it wants to investigate.
The UFO has infinite acceleration but is limited to a speed of ( altitude + 1km ) / 100 / sec. (Example: at ground level it can travel 10m/s. At 1km altitude it can travel 20m/s.)
What flight plan will get the UFO to his destination the soonest possible?
(You can ignore curvature of the earth, variance in terrain, and so on. Put the UFO at (1,1) on a graph and fly him to (0,0) if you want.)