A surveyor models a hillside's height as h(x,y) = 180 - 0.03x^2 - 0.08y^2 m

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Vector calculus and field geometry · Vector calculus and field geometry

Mathematical Methods for Physics, Ch Gradient, divergence and curl

Problem

A surveyor models a hillside's height as h(x,y)=180−0.03x2−0.08y2 m,h(x,y) = 180 - 0.03x^2 - 0.08y^2\ \mathrm{m}, where xx is the distance in metres east and yy the distance in metres north of a signpost on the summit. At the point (50 m,10 m)(50\ \mathrm{m}, 10\ \mathrm{m}): ((a)) Find ∇h\nabla h, and state the steepest slope and its direction as a compass bearing (measured clockwise from north). ((b)) Find the rate at which the ground rises, in metres per metre, walking north-west from this point.

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