Classical Dynamics of Particles and Systems · Problem 1-40

Newtonian Mechanics—Single Particle — Marion & Thornton

Physics — Mechanics · gradient-operator

Problem

The height of a hill in meters is given by

z = 2xy - 3x^2 - 4y^2 - 18x + 28y + 12

, where

x

is the distance east and

y

is the distance north of the origin. ((a)) Where is the top of the hill and how high is it? ((b)) How steep is the hill at

x = y = 1

, that is, what is the angle between a vector perpendicular to the hill and the

z

axis? ((c)) In which compass direction is the slope at

x = y = 1

steepest?