Consider a problem analogous to the varying wind velocities encountered by transcontinenta...

Consider a problem analogous to the varying wind velocities encountered by transcontinental aircraft. We assume a constant altitude, a plane earth, a flight along the x axis from 0 to 10 units, no vertical velocity component, and no change in wind velocity with time. Assume ax to be directed to the east and ay to the north. The wind velocity at the operating altitude is assumed to be:

Determine the location and magnitude of (a) the maximum tailwind encountered; (b) repeat for headwind; (c) repeat for crosswind; (d) Would more favorable tailwinds be available at some other latitude? If so, where?