Rain Gutter

You wish to construct a rain gutter from a long strip of metal by bending up equal width strips on either edge.The diagram shows a cross-section of the gutter. Using the sliders you can adjust the width of the base of the gutter as well as the width of the bent up side strips. You can adjust the angle of the side strips by dragging the RED dot. How does the amount of water the gutter can carry vary with the angle shown in the diagram? Does your solution behave reasonably in limiting cases? in obvious cases? Does your solution correctly predict the angle for which the carrying capacity of the gutter is maximum? What problems could/would you set for your students based on this applet? Adapted from "Calculus: The Analysis of Functions" by P.D. Taylor