Exploring where trajectories crest
For a projectile fired from the ground with a launch angle and an initial velocity , consider the launch angle to be variable and the initial velocity to be fixed. As the launch angle varies from 0 to , the maximum heights of the resulting trajectories lie on an ellipse.
In the interactive figure, drag point to change the launch angle of the projectile. Drag point to change the initial velocity, . The highest point on the trajectory for a given initial velocity lies on an ellipse.
Developed for use with Thomas' Calculus, published by Pearson.