### Pemodelan Matematika Tendangan Penalti Pada Olahraga Futsal

Hagi Gusmaldy - Mathematics Department Universitas Negeri Padang
Yusmet Rizal - Mathematics Department Universitas Negeri Padang

#### Abstract

Abstract— Penalty is the best chance to score in a set play situation. The kicker is almost unmatched by anyone except the enemy goalkeeper who is 6 meters away from the kicker. The problem that occurs with this penalty kick is that most players are more concerned with the power of the shot compared to the direction of the ball to a point that is difficult to reach by the goalkeeper, so that many kickers fail to take kicking shots in this futsal sport. The purpose of this study is to determine a mathematical model and interpret the model obtained. This mathematical model is obtained with a range of angles defined using right triangles and trigonometric ratios. Also, the sides of the triangle are calculated using the Pythagorean theorem. Velocity is calculated using a simple projectile motion equation. The numerical method is used to find the velocity range for each corner. The result of the research is that the initial velocity of the ball is 78, 19 km / h, while the angles for each are θ = 38,14o  or  θ = 51,86o.

Keyword —mathematical model, penalty kick, futsal, angel, velocity.

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DOI: http://dx.doi.org/10.24036/unpjomath.v5i3.10595