Question bank: Invasion Sports

During a school tournament of invasion sports, several teams compete in handball matches. In one of the matches, an athlete throws the ball towards the opponent's goal with an initial velocity of 14 m/s at an angle of 30° relative to the horizontal plane. Disregarding air resistance and considering gravity acceleration as 10 m/s², what is the maximum height the ball reaches relative to the launch point? Knowledge of projectile trajectories is essential for understanding the performance of throws and launches in sports like handball.

During a theoretical class on strategies and tactics in invasion sports, a Physical Education teacher presented to the students an excerpt from the book 'The Talent Lab: The Secret to Creating and Sustaining Success' by Owen Slot, which discusses the importance of communication and collective understanding for a team's success in rugby. From this reflection, analyze the following statement: 'In invasion sports, communication among players is an essential element for the effectiveness of strategies and the achievement of game objectives.' Interpret the role of communication in these sports and relate it to game dynamics and possible interactions with the disciplines of Linguistics and Psychology.

During an intercollegiate championship, a group of 3rd-year high school students decides to organize an 'Ultimate Frisbee' competition in which teams are formed in such a way that each team has an equal number of male and female players to promote gender equity and inclusion in the sport. As the student Pedro noticed that, in general, there are more male students than female students in the championship, he proposed a strategy to organize the teams in a way that, considering the total number of players and the gender ratio, all teams have the highest possible number of male and female players, maintaining equity. Assuming there are 72 students registered in the championship and the ratio of male to female players is 3 to 2, what would be the gender composition of each team, and how many teams can be formed following Pedro's proposal? Additionally, Pedro raised the issue that in previous championships, matches often started with players incorrectly positioned on the field, due to an insufficient understanding of the positioning rules. Based on the rules of Ultimate Frisbee, which require each team to start with seven players on the field, and that alternating teams must start in opposite positions, sketch a diagram representing the initial arrangement of male and female players on one of the teams, and explain how knowledge of these rules can help avoid errors in team formation.

During a study on game strategies in invasion sports, a group of 3rd-year high school students decided to analyze how variations in the launch angle and speed of a ball affect the trajectory and reach of a pass in different circumstances. They used the concept of oblique projectile motion from Physics, which describes the movement of an object projected both horizontally and vertically, and applied the laws of Analytical Geometry to model the trajectories with parametric equations. Considering a field of known dimensions and aiming to make a soccer pass that covers the greatest distance possible, without disregarding air resistance and assuming the field is flat and without inclination, the students need to determine the ideal conditions (launch angle and speed) for the pass. Additionally, they want to compare these conditions with those of a straight pass, disregarding air resistance. Based on the laws of Physics, describe the steps to solve this problem, justifying the choices made at each step and identifying the formulas or physical principles involved.

During a soccer match, a player takes a penalty kick from a distance of 12.0 m from the center of the goalpost, which has a width of 7.32 m. Considering the kick as an oblique projectile motion and neglecting air effects, determine the initial velocity with which the ball must be kicked so that, after covering half of the distance to the goal, its height is 2.44 m, passing exactly at the point where the height of the crossbar begins. Additionally, assuming a crosswind speed of 5.0 m/s, determine the direction in degrees at the moment of the kick so that the ball, after overcoming the influence of the wind and without further deviations, reaches the intersection of the crossbar and the vertical bar of the goal. Consider the coordinates (0,0) at the penalty kick launch point.