Modelling Football Penalty Kicks

dc.creator	Jeffrey K. Leela
dc.creator	Donna M. G. Comissiong
dc.date	2009-05-01T00:00:00Z
dc.date.accessioned	2015-07-20T22:13:09Z
dc.date.available	2015-07-20T22:13:09Z
dc.identifier	1870-9095
dc.identifier	https://doaj.org/article/d780e858703c4b309a5de9ce869b68c8
dc.identifier.uri	http://evidence.thinkportal.org/handle/123456789/15802
dc.description	AbstractIn modern football the penalty kick is considered a golden opportunity for the kicker to register a goal. The kicker isvirtually unchallenged by any opposing player except the goalkeeper who stands on the goal-line 12 yards away.Therefore, the kicker has an overwhelming advantage. Maximising on this advantage is of paramount importancesince penalties in many instances, determine the outcome of games. This paper analyses the variables involved in apenalty kick and attempts to devise the best method to kick a penalty to ensure a very high success rate. The twofundamental components of a penalty shot are the angle at which the shot is kicked and the velocity of the shot. Afeasible range of angles is established using right angled triangles and trigonometric ratios. Also, the sides of thesetriangles are calculated using Pythagoras theorem. Velocities are calculated using simple projectiles motion equations.Numerical methods are employed to find the range of velocities for the respective angles. The penalty kicks modelledin this thesis are high velocity shots placed in areas of the goal that are difficult for goal-keepers to reach. Theseresults inform coaches about the techniques used to kick a penalty with the required trajectory. Players can practisethese techniques to develop mastery. It is also important to mention the educational impact this project can have onthe teaching of calculus to undergraduates. Interest is generated with the use of real world examples that appeal tostudents who like sports and provides a foundation for research in Applied Mathematics. This can be described as asimple and stimulating introduction to the technique of Mathematical Modelling.
dc.language	English
dc.language	Spanish
dc.language	Portuguese
dc.publisher	Instituto Politécnico Nacional, Latin American Physics Education Network
dc.relation	http://www.journal.lapen.org.mx/May09/LAJPE%20239%20preprint%20f.pdf
dc.relation	https://doaj.org/toc/1870-9095
dc.source	Latin-American Journal of Physics Education, Vol 3, Iss 2, Pp 259-269 (2009)
dc.subject	Penalty kick
dc.subject	goalkeeper
dc.subject	angle
dc.subject	velocity
dc.subject	trajectory
dc.subject	football
dc.subject	mathematical modelling.
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	DOAJ:Education
dc.subject	DOAJ:Social Sciences
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	DOAJ:Education
dc.subject	DOAJ:Social Sciences
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.title	Modelling Football Penalty Kicks
dc.type	article