(Originais Teachy 2024) - Question Hard of Physical Education

During an interdisciplinary class, 7th-grade students are learning about the sport of darts in the context of physics mechanics and geometry mathematics. Considering a dartboard divided into 20 different scoring segments, where each segment has an associated score and there are also rings that multiply this score, a student throws a dart that, after a parabolic trajectory, hits the target at a precise point. The teacher, taking advantage of the situation, asks the students to calculate the exact distance between the throwing point and the center of the target, knowing that the dart hit the highest scoring segment of the target and considering the standard rules of the game of darts that establish that the central segment of the target has the highest scoring value and the target is fixed at a height that allows the dart's trajectory to be modeled by a parabola. Additionally, the force and angle of dart throwing are provided as functions of trigonometric variables, and any air effects are disregarded. Based on this information, determine the exact distance between the throwing point and the center of the target.