Abstract
On the final day of Galileo’s Dialogues, Salviati, Sagredo and Simplicio draw upon their previous work on uniform motion and naturally accelerated motion in order to better understand the motion of projectiles. What, they ask, is the trajectory of a cannonball which has been fired horizontally? And how can one compute its speed at any point along its trajectory? Before answering these questions, they must recall the work of the ancient geometer Apollonius.
Their assumptions were not false, and therefore their conclusions were absolutely correct.
—Galileo Galilei
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Notes
- 1.
A very near approach to Newton’s Second Law of Motion. [Trans.].
- 2.
For a comprehensive theoretical treatment of fluid flow and Reynolds number, see Chaps. 4.7 and 4.12 of Batchelor, G. K., An Introduction to Fluid Mechanics, Cambridge University Press, 1967. A more recent treatment of the same subject is provided in Chap. 1 of Frisch, U., Turbulence, Cambridge University Press, 1995. A pleasant discussion of the Reynolds number from a life-science perspective can also be found in Chaps. 5 and 15 of Vogel, S., Life in Moving Fluids, 2 ed., Princeton University Press, 1994.
- 3.
See, for example, T.A. Johnson, and Patel, V.C., Flow past a sphere up to a Reynolds number of 300, Journal of Fluid Mechanics, 378, 19–70, 1999.
- 4.
Regrettably, the drag coefficient also depends on the flow velocity, so the apparent u 2 dependence of Eq. 11.3 is a bit misleading.
- 5.
Galileo briefly discussed the effect of buoyancy and drag on falling bodies on page /119/ of his Dialogues. This discussion can be found in Chap. 3 of the present volume.
- 6.
For example, the Mini Launcher (Model 6825 A), Pasco, Inc., Roseville, CA.
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Kuehn, K. (2015). From Conic Sections to Projectile Motion. In: A Student's Guide Through the Great Physics Texts. Undergraduate Lecture Notes in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1366-4_11
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