This paper considers a model of free fall in the troposphere (altitude of up to 11 km) that takes into account the decrease of the air density, temperature, and the speed of sound. Two cases are analyzed: The maximum speed is less than Mach 0.8 (subsonic fall) for which the drag coefficient is constant, and the maximum speed exceeds Mach 0.8 (transonic and supersonic fall) for which the drag coefficient depends on the speed. The equation of motion is solved analytically for subsonic fall, and the range of validity of the solution is found. The solution for supersonic fall in the troposphere is found for the free fall of a bomb. The drag coefficient function is obtained by a least square fit to measured data, and the differential equation is solved numerically.
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June 2010
PAPERS|
June 01 2010
High-altitude free fall revised
Jan Benacka
Faculty of Natural Sciences,
Constantine the Philosopher University
, Tr. A Hlinku 1, SK-94974 Nitra, Slovakia
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Electronic mail: jbenacka@ukf.sk
Am. J. Phys. 78, 616–619 (2010)
Article history
Received:
September 24 2009
Accepted:
January 04 2010
Citation
Jan Benacka; High-altitude free fall revised. Am. J. Phys. 1 June 2010; 78 (6): 616–619. https://doi.org/10.1119/1.3298375
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