Calculus III

What is the maximum range of a cannon that sits on a cliff h feet above the ground and fires a projectile with magnitude of initial velocity v? First you need the parameterization of the position of the projectile r. Use theta for the angle of elevation.

a) Set this problem up to be solved with LaGrange multipliers. Give a f(t, theta) to be maximized. And give a constraint equation, g(t, theta)=c.

b) Give the system of three equations that comes from the Lagrange multipliers procedure.

Question

Calculus III

What is the maximum range of a cannon that sits on a cliff h feet above the ground and fires a projectile with magnitude of initial velocity v? First you need the parameterization of the position of the projectile r. Use theta for the angle of elevation. 

a) Set this problem up to be solved with LaGrange multipliers. Give a f(t, theta) to be maximized. And give a constraint equation, g(t, theta)=c.

b) Give the system of three equations that comes from the Lagrange multipliers procedure.