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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

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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.

Information

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

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