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 a_xto be directed to the east and a_yto 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?

(0.01.x2 v(x, y) = 0.08x +0.66)a, (0.05x 0.4)a, 1+0.5y2