Tartaglia's Bet

Abstract

We discuss an episode in the early history of ballistics and employ elementary calculus to settle an old bet (at least in a simple case). Specifically, for a model of projectile motion in which the resistive force is proportional to the velocity an explicit formula is derived for the optimal angle of projection. This formula involves a log-like function and gives the optimal angle in terms of a single dimensionless parameter that incorporates all of the physical constants in the model.