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.
@article{1644,
title = {Tartaglia's Bet},
journal = {CUBO, A Mathematical Journal},
volume = {6},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/1644}
}
Groetsch, C.W. Tartaglia's Bet. CUBO, A Mathematical Journal, Tome 6 (2004) . http://gdmltest.u-ga.fr/item/1644/