Final answer:
A Ferris Wheel's movement can be modeled by a sinusoidal function, with the height varying between 2 and 18 meters and a midline at 10 meters. The period of the function corresponding to the time for one revolution is 60 seconds, and the height function is h(t) = 8 sin(2π/60 t) + 10.
Step-by-step explanation:
The Ferris wheel problem is a classic application of trigonometric functions, specifically sinusoidal functions in mathematics. The wheel's radius is 8 meters and it makes a full revolution in 60 seconds, with the lowest boarding point at 2 meters above the ground. Therefore, at the lowest point, the height of a car is 2 meters, and at the highest point, it is 2 meters (ground level) + 8 meters (radius) * 2 = 18 meters. Due to the sinusoidal nature of the movement, the midline of the function is at 10 meters.
Since the Ferris wheel makes a full revolution in 60 seconds, we can define the period of the function as 60 seconds. The function for height h(t), as a function of time t, in seconds, after boarding would then be:
h(t) = 8 sin(2π/60 t) + 10, with the midline at y = 10, minimum at (t, h) = (0, 2), and maximum at (t, h) = (30, 18). The function starts at the minimum value because that is the boarding height, then reaches the maximum at half the period (30 seconds), before returning to the minimum at the full period (60 seconds).