Analytical Investigation of Projectile Motion in Midair
DOI:
https://doi.org/10.24297/jap.v13i6.6167Keywords:
Classic problem, projectile motion, quadratic drag force, analytic formulasAbstract
Here is studied a classic problem of the motion of a projectile thrown at an angle to the horizon. The air drag force is taken into account as the quadratic resistance law. An analytic approach is used for the investigation. Equations of the projectile motion are solved analytically. All the basic functional dependencies of the problem are described by elementary functions. There is no need for to study the problem numerically. The found analytical solutions are highly accurate over a wide range of parameters. The motion of a baseball and a badminton shuttlecock are presented as examples.
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References
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37 (2016), 035001.
[2] C. Belgacem, Range and flight time of quadratic resisted projectile motion using the Lambert W function, Eur. J. Phys. 35 (2014), 055025.
[3] A. Vial, Horizontal distance travelled by a mobile experiencing a quadratic drag force: normalized distance and parameterization, Eur. J. Phys. 28 (2007), pp. 657-663.
[4] G.W. Parker, 1977 Projectile motion with air resistance quadratic in the speed, Am. J. Phy. 45 (1977), pp. 606-610.
[5] K. Yabushita, M. Yamashita, and K. Tsuboi, 2007 An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method, J. Phys. A: Math. Theor. 40 (2007), pp. 8403-8416.
[6] P. Chudinov, The motion of a heavy particle in a medium with quadratic drag force, Int. J. Nonlinear Sci. Numer. Simulat. 3 (2002), pp. 121-129.
[7] P. Chudinov, Approximate analytical investigation of projectile motion in a medium with quadratic drag force, Int. J. Sports Sci. Engin. 5 (2011), pp. 27 – 42.
[8] P. Chudinov, Analytical investigation of point mass motion in midair, Eur. J. Phys. 25 (2004), pp. 73- 79.
[9] B. N. Okunev, Ballistics, Voyenizdat, Ðœoscow, 1943.
[10] S. Timoshenko, D. H. Young, Advanced Dynamics, McGrow-Hill Book Company, New York, 1948.
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Published
2017-06-01
How to Cite
Chudinov, P., Eltyshev, V., & Barykin, Y. (2017). Analytical Investigation of Projectile Motion in Midair. JOURNAL OF ADVANCES IN PHYSICS, 13(6), 4919–4926. https://doi.org/10.24297/jap.v13i6.6167
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