Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-21T10:22:11.147Z Has data issue: false hasContentIssue false
  • English
  • Français

Launching a projectile to cover maximal area

Published online by Cambridge University Press:  06 June 2019

Robert Kantrowitz  and
Michael M. Neumann
Robert Kantrowitz
Affiliation:
Department of Mathematics, Hamilton College, 198 College Hill Road, Clinton, NY 13323, USA e-mail: rkantrow@hamilton.edu
Michael M. Neumann
Affiliation:
Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA e-mail: neumann@math.msstate.edu
Get access Rights & Permissions [Opens in a new window]

Extract

The launch and subsequent motion of a projectile provide a context for several quantities that yearn to be optimised. Most notable is the horizontal range of the projectile, a problem dating back to Galileo and still studied in modern times; see, for example [1], [2], [3], [4]. In a different direction, the articles [5] and [6] provide a solution to the problem of finding the angle of launch that results in the trajectory of longest arc length.

Type
Articles
Information
The Mathematical Gazette , Volume 103 , Issue 557 , July 2019 , pp. 277 - 284
Copyright
© Mathematical Association 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

de Mestre, N., The mathematics of projectiles in sport, Cambridge University Press (1990).10.1017/CBO9780511624032CrossRefGoogle Scholar
Kantrowitz, R. and Neumann, M. M., Optimal angles for launching projectiles: Lagrange vs. CAS, Can. Appl. Math. Q. 16(3) (2008) pp. 279-299.Google Scholar
Kantrowitz, R. and Neumann, M. M., Let’s do launch: more musings on projectile motion, Pi Mu Epsilon J. 13(4) (2011) pp. 219-228.Google Scholar
Kantrowitz, R. and Neumann, M. M., Some real analysis behind optimization of projectile motion, Mediterr. J. Math. 11(4) (2014) pp. 1081-1097.CrossRefGoogle Scholar
Cooper, J. and Swifton, A., Throwing a ball as far as possible, revisited, Amer. Math. Monthly 124(10) (2017) pp. 955-959.CrossRefGoogle Scholar
Tan, A. and Giere, A. C., Maxima problems in projectile motion, Am. J. Phys. 55(8) (1987) pp. 750-751.CrossRefGoogle Scholar
Troutman, J. L., Variational calculus with elementary convexity, Springer-Verlag, New York (1983).CrossRefGoogle Scholar
Perkins, D., Calculus and its origins, Mathematical Association of America, Washington, DC (2012).CrossRefGoogle Scholar
Stahl, S., Real analysis: a historical approach (2nd edn.), Wiley (2011).10.1002/9781118096864CrossRefGoogle Scholar