(Originais Teachy 2023) - Question Hard of Physical Education

In Physical Education class, 2nd grade students were challenged to practice a sport that requires precision and motor coordination. Using a lighter dart adapted to their age, they should throw it towards a target painted on the ground, trying to hit the center. The teacher noticed that many students were having difficulty adjusting the throwing force to hit the desired target, so he decided to teach a strategy. He explained that to hit the center of the target, it was necessary to consider the distance, the weight of the dart, and the thrower's strength. Taking these aspects into account, the teacher asked the students to calculate the ideal launch angle so that the dart would cover most of the distance in the air, staying close to the ground, thus avoiding significant deviation in its trajectory caused by gravitational force. As the students were learning about the effects of gravity and the influence of parabolic trajectory on throws, the teacher introduced the following question: 'If a student must throw the dart a distance of 5 meters, and considering that the dart will be thrown from a height that does not significantly affect its range, what should be the launch angle for the dart to hit the ground as close as possible to the target without surpassing it?'