Question

A car is driving northwest at vv mph across a sloping plain whose height, in feet above sea level, at a point nn miles north and ee miles east of a city is given by

Answer 1

Northwest is 45 degrees north of west. If a car travels a distance x miles northwest, its northerly component gains x/sqrt(2) miles and its easterly component LOSES xsqrt(2)/ miles.

Resultant height is h = 4500 + 100x/sqrt(2) - 75x/sqrt(2) = [25/sqrt(2)]x + 4500
dh/dt = [25/sqrt(2)]dx/dt = [25/sqrt(2)]v