Chapter 1, Problem 1.30P

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_x to be directed to the east and a_y to the north. The wind velocity at the operating altitude is assumed to be:

$V\left(x,y\right)=\frac{\left(0.01x^2-0.08x+0.66\right)a_x-\left(0.06z-0.4\right)a_y}{1+0.5y^2}$

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?