Toy Cannon

A toy cannon can fire a ball. The goal is to find what angle will give the greatest distance for the ball. Adjust the angle then click Fire to see the path of the ball. The height of the ball is given by and the horizontal position by .
This is an optimization problem where you want to find the maximum distance based on the firing angle. In this applet you can use trial and error to find the angle but with a little calculus you can solve for the optimal angle. Check your results with this applet where