Soccer Penalty Kicks

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This Demonstration shows the trajectories of a goalkeeper and a soccer ball in 3D.


Adjust the position, velocity, and angle of your penalty kick to try and score a goal. The keeper's reaction time and speed are based on real-life data. If the trajectory of the soccer ball is intercepted by the trajectory of the keeper, a save is made.


Contributed by: Daniel Classon and Josh Seidman (June 2016)
Open content licensed under CC BY-NC-SA



Snapshot 1: The ball is in midair after shooting it (tracking sphere enabled)

Snapshot 2: The ball has made it into the goal before the keeper was able to get there, resulting in a goal

Snapshot 3: The keeper was able to save the ball before it got to the goal, resulting in a save

To create a realistic Demonstration, we found as much real-life data to incorporate as possible, including an average goalkeeper speed of 15 mph (6.7 m/s), an average kick speed of 60 mph (26.8 m/s), and goalkeeper reaction time of 0.3 seconds.

You can place the player anywhere in the penalty box and change the zenith and azimuth angles (the elevation and side-to-side angles, respectively). If the ball's trajectory goes into the goal, then it is a goal! But if the ball's trajectory does not go into the goal, or the keeper's trajectory intersects with the ball, it is a save.

Special thanks to the University of Illinois NetMath Program and the mathematics department at William Fremd High School.


[1] M. Knoop, J. Fernandez-Fernandez, and A. Ferrauti, "Evaluation of a Specific Reaction and Action Speed Test for the Soccer Goalkeeper," Journal of Strength and Conditioning Research, 27(8), 2013 pp. 1241–2148. doi:10.1519/JSC.0b013e31827942fa.

[2] S. Khan. "Thiago Asks: How Much Time Does a Goalkeeper Have to React to a Penalty Kick?." (Jun 9, 2016)

[3] G. Mihoces. "Stopping a Soccer Penalty Kick Is Quite a Feat." (Jun 9, 2016)

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