October 22, 2022
VT Northern Virginia Center
US/Eastern timezone
We thank all attendees for making the meeting such a great success. See you all in Harrisonburg on April 1, 2023!

Optimal launch angles: Novel perspectives of an ancient problem

Oct 22, 2022, 10:00 AM
Room 214 (VT Northern Virginia Center)

Room 214

VT Northern Virginia Center

7054 Haycock Rd, Falls Church, VA 22043


Prof. R. K. P. Zia (Virginia Tech)


We revisit the ancient problem of finding the optimal angle for launching a projectile so as to maximize the range. In the last meeting, we showed a solution to this problem using only geometry. Here, we present some novel perspectives. One is the notion of "duality" (between the launch and target sites). Another is the envelope of all trajectories (for launching at different angles, but with the same speed). Consequences associated with these ideas are explored. If time permits, we will show a simple, unified approach that includes launches on a spherical earth. Relying only on energy conservation and properties of ellipses/parabolas, this approach should lie within the grasp of high school students.

Primary authors

Prof. Michael J. Ruiz (University of North Carolina at Asheville) Prof. R. K. P. Zia (Virginia Tech)

Presentation materials