Mathematics of soccer: Shot angles

Consider a situation in which a soccer player runs straight, with tha ball, towards the bottom line of the field. Intuitively, it is clear that there is an optimal point maximizing the shot angle, providing the best place to kick in order to improve the chances to score a goal. If the player chooses the bottom line, the angle is zero and his chances are just horrible; if the player kicking far way, tha angle is also too small!

Locus of the optimal points
Two different types of kicks: Diego Armando Maradona in Napoli-Cesena 2-0, Serie A 1987/88, an amazing example of the "Maradona feeling" about the optimal place to kick
and the "impossible" goal by Marco Van Basten during the final of Euro '88

from "Mathematics of Soccer" by Alda Carvalho, Carlos Pereira dos Santos, Jorge Nuno Silva. "Recreational Mathematics Magazine" (2014)

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