## Early perceptions of projectile motion

Stories from Physics for 11-14 14-16

In 1537, Nicolò Tartaglia, an Italian mathematician, published *Nova Scientia*, a work that has subsequently been recognised as the foundational text in ballistics. Tartaglia, through calculation and observation, reported that the maximum range of a cannon occurred at an angle of 45°. However, his understanding differs from modern models of projectile motion — Tartaglia assumed that the trajectory of a cannon ball could be approximated using straight lines and circular arcs. He may have been inspired by representations of projectile motion from the Middle Ages that represented trajectories with an initial linear section, followed by a circular arc and then a final vertical descent. Though these descriptions of motion seem clearly mistaken to modern eyes, they approximate well to the motion of projectiles when drag forces act. The description of the path of a projectile as parabolic emerged from experiments that are reported to have been carried out jointly by Galileo and his patron, Guidobaldo del Monte, by rolling a ball dipped in ink across an inclined plane to establish the geometrical form of projectile motion.

### References

F. J. Swetz, An historical example of mathematical modelling: the trajectory of a cannonball. International Mathematical Education in Science and Technology, vol. 20, no, 5, 1989, 731-741, pp. 734

P. La Rocca, & F. Riggi, Projectile motion with a drag force: were the Medievals right after all? Physics Education, vol. 44, no. 4, 2009, pp. 398-402.

R. H. Naylor, Galileo’s theory of projectile motion. Isis, vol. 71, no. 4, 1980, pp. 550-570, p. 551

S. Drake, Galileo at Work: His Scientific Biography, Mineola, NY, Dover Publications, Inc., 2003, p. 1608