Observations of gravitational free fall during drop experiments support a quadratic model
DOI:
https://doi.org/10.64804/bzdpzs95Keywords:
data analysis, regression, kinematics, gravity, acceleration, quadratic, free fall, R, ggplot2, dplyrAbstract
When an object is dropped, standard kinematics predicts that in the absence of resistive forces, the vertical distance it travels due to gravity is described quadratically with respect to time. In this experiment, we dropped a tennis ball with negligible initial velocity from various known test heights and recorded the fall time for each trial. We then assessed whether our data were consistent with the predictions of standard kinematics, ultimately finding evidence that our height vs time data is compatible with the constant acceleration assumption of kinematics with a gravitational acceleration of magnitude 9.4 ± 0.3 m/s2 .
References
P. A. Tipler and G. Mosca, Physics for Scientists and Engineers, 5th ed. (W H Freeman and Company, New York, 2004).
W. Moebs, S. J. Ling, and J. Sanny, University Physics, Vol. 1 (OpenStax, Houston, TX, 2016).
R. A. Pelcovits and J. Farkas, Barron’s AP Physics C Premium (Kaplan North America, Fort Lauderdale, FL, 2024).
R. Larson and R. P. Hostetler, Calculus, 8th ed. (Brooks Cole, Pacific Grove, CA, 2005).
D. S. Starnes, J. Tabor, D. Yates, and D. S. Moore, The Practice of Statistics, 5th ed. (W. H. Freeman and Company, 2015).
R Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria (2025).
H. Wickham, R. François, L. Henry, K. Müller, and D. Vaughan, dplyr: A Grammar of Data Manipulation (2026), R package version 1.2.0.
H. Wickham, ggplot2: Elegant Graphics for Data Analysis (Springer-Verlag New York, 2016). DOI: https://doi.org/10.1007/978-3-319-24277-4_9
G. Galilei, Discorsi e dimonstrazioni matematiche, intorno à due nuoue scienze attenenti alla mecanica & i movimenti locali (1638).
R. K. Hetzler, C. D. Stickley, K. M. Lundquist, and I. F. Kimura, Reliability and accuracy of handheld stopwatches compared with electronic timing in measuring sprint performance, Journal of Strength and Conditioning Research 22, 1969 (2008). DOI: https://doi.org/10.1519/JSC.0b013e318185f36c
D. A. Faux and J. Godolphin, Manual timing in physics experiments: error and uncertainty, American Journal of Physics 87, 110 (2019). DOI: https://doi.org/10.1119/1.5085437
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Data are available at https://github.com/devangel77b/427jcardillo-lab1
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