QuestionThe radius of a Ferris wheel is 260 ft . The entry platform is 30 ft above the ground. As the Ferris wheel rotates, the height above the ground of each individual rider follows a sinusoidal pattern, as shown below.
If the ground level is the reference point, the amplitude and median of the sinusoidal function are respectively,
Select one:
a. 260 and 260
b. 520 and 260
c. 260 and 290
d. 230 and 290
Studdy Solution
STEP 1
1. The Ferris wheel is circular with a radius of feet.
2. The entry platform is feet above the ground.
3. The height of a rider follows a sinusoidal pattern.
STEP 2
1. Determine the amplitude of the sinusoidal function.
2. Determine the median (vertical shift) of the sinusoidal function.
3. Select the correct answer from the given options.
STEP 3
Determine the amplitude of the sinusoidal function:
The amplitude of a sinusoidal function is the distance from the midline to the maximum or minimum value. Since the radius of the Ferris wheel is feet, the amplitude is equal to the radius:
STEP 4
Determine the median (vertical shift) of the sinusoidal function:
The median (or midline) of the sinusoidal function is the average height above the ground. The Ferris wheel's center is at the height of the radius plus the height of the entry platform:
STEP 5
Select the correct answer from the given options:
The amplitude is and the median is . Thus, the correct answer is:
c. 260 and 290
The correct answer is:
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