The trajectory of a ball in air is affected by aerodynamic drag and lift. In general, the trajectory needs to be calculated numerically since the acceleration varies with time in both the horizontal and vertical directions. If the trajectory remains approximately parabolic, then simple analytical solutions can be found, giving useful insights into the behavior of the ball as it travels through the air.

1.
Rod
Cross
and
Crawford
Lindsey
, “
Measuring the drag force on a falling ball
,”
Phys. Teach.
52
,
169
170
(March
2014
).
2.
Alan
Nathan
, “
The effect of spin on the flight of a baseball
,”
Am. J. Phys.
76
,
119
124
(Feb.
2008
).
3.
David
Kagan
and
Alan
Nathan
, “
Statcast and the Baseball Trajectory Calculator
,”
Phys. Teach.
55
,
134
136
(March
2017
).
4.
David
Kagan
, “
The anatomy of a pitch: Doing physics with PITCHf/x data
,”
Phys. Teach.
47
,
412
416
(Oct.
2009
).
5.
Rod
Cross
,
Physics of Baseball and Softball
(
Springer
,
New York
,
2011
).
6.
A.
Stepanek
, “
The aerodynamics of tennis balls –The topspin lob
,”
Am. J. Phys.
56
,
138
141
(Feb.
1988
).
7.
Peter
Dewhurst
,
The Science of the Perfect Swing
(
Oxford University Press
,
2015
).
8.
John
Goff
and
Matt
Carre
, “
Trajectory analysis of a soccer ball
,”
Am. J. Phys.
77
,
1020
1027
(Nov.
2009
).
9.
David
Kagan
and
Alan
Nathan
, “
Simplified models for the drag coefficient of a pitched baseball
,”
Phys. Teach.
52
,
278
280
(March
2014
).
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