Every introductory physics student studies projectile motion where the gravitational acceleration is constant. Many articles highlight interesting features not discussed in the texts. For example, one can find analyses of projectile trajectories to determine the firing angle leading to the maximum path length or to determine the average speed.1–3 Similarly, one can find descriptions of “hidden” ellipses or circles found when one compares the trajectories of projectiles fired at different angles.4–7 One can even find a geometrical proof for why maximum range is achieved when the initial and final velocities are perpendicular.8 In this work, we examine the surprising behavior of the projectile’s distance from the origin (r) during its flight and provide some exercises for your students.
This problem is from Young and Freedman’s text9:
This challenging problem is appropriate for physics majors and/or honors students. It helps them practice their calculus...
