Final answer:
Corey's height above the ground as he rides the Ferris wheel can be modeled by the function g(θ) = 15 + 10 sin(θ), with the initial height being 15 meters.
Step-by-step explanation:
To define a function g that expresses Corey's distance above the ground in terms of the number of radians θ the angle has swept out since the ride started, we consider the motion of Corey on the Ferris wheel as sine wave oscillation, due to the circular motion.
At the 3-o'clock position, Corey is 15 meters above the ground and directly at the edge of the wheel's circle. Since the radius of the Ferris wheel is 10 meters, the center of the wheel is at a height of 10 meters (the radius) + 5 meters (the difference between Corey's starting height and the radius) for a total of 15 meters above the ground.
The function g(θ) = 15 + 10 sin(θ) models the vertical position of Corey above the ground in meters. This is because Corey's height varies as a sine function of the angle θ. Here, the amplitude is 10 (the radius of the Ferris wheel), and the vertical shift is 15 (the center's height above the ground). The function g(0) is the initial height of Corey above the ground, so g(0) = 15 + 10 sin(0) = 15 meters.