Final answer:
The minimum height above the ground on the Ferris wheel is 5 feet, and the maximum height is 55 feet, as determined by subtracting and adding the amplitude of the sine function to the vertical shift of the equation h=25sin(π/15(t−75))+30.
Step-by-step explanation:
The question involves determining the minimum and maximum heights above the ground as you ride a Ferris wheel modeled by the equation h=25sin(π/15(t−75))+30. This equation is a sinusoidal function that oscillates between a minimum and maximum value based on the amplitude and the vertical shift. The amplitude is the coefficient in front of the sine function, and the vertical shift is the constant added at the end. In this case, the amplitude is 25 feet and the vertical shift is 30 feet.
To find the minimum height, you take the vertical shift and subtract the amplitude, resulting in 30 feet - 25 feet = 5 feet. This is because the sine function has a minimum value of -1, and when multiplied by the amplitude and adjusted by the vertical shift, it gives us the lowest point of the ride.
To find the maximum height, you add the amplitude to the vertical shift, resulting in 30 feet + 25 feet = 55 feet. This is because the sine function has a maximum value of 1, and when multiplied by the amplitude and adjusted by the vertical shift, it provides the highest point. Therefore, the minimum height you can be above the ground on the Ferris wheel is 5 feet, and the maximum height is 55 feet.