(Originais Teachy 2024) - Question Easy of Mathematics

During a Physics class, a group of students decides to analyze the movement of a Ferris wheel to determine the maximum height that one of its cabins reaches. Considering that the diameter of the Ferris wheel is 50 meters and that, in the initial position, the cabin is 25 meters above the ground, they want to calculate the maximum height reached by this cabin during a complete cycle of movement. Knowing that the height of the cabin relative to the ground can be modeled by a sinusoidal function, the students choose a coordinate system in which the center of the Ferris wheel corresponds to the origin and the positive vertical axis points upwards. If the movement is described by the function h(t) = A * sin(Bt + C) + D, where h(t) is the height of the cabin at time t, A is the amplitude of the movement, B influences the period of the movement, C represents the initial phase of the movement, and D is the vertical equilibrium position, determine the function that describes the height of the cabin relative to the ground and calculate the maximum height reached by it. Consider that the complete up and down movement of the Ferris wheel is done in π/2 hours.