Answer:
The change in the height of the seat of the Ferris wheel is a reduction in height of approximately 74.25 feet
Step-by-step explanation:
The given information are;
The position of the seat on the Ferris wheel = The center level of the wheel
The diameter of the Ferris wheel = 210 feet
The angle of rotation of the wheel = 45° counterclockwise
The height of a point on the Ferris wheel is given by the relation;
h = A·cos(b·x + c) + d
With regards to the question, we have;
h = The height of the seat of the Ferris wheel
A = The amplitude = 1/2 × The diameter of the wheel = 210/2 = 105 feet
360/b = The period
c = The phase shift = 90°
d = The mid line = 0
For a rotation of 45° counterclockwise or-45° clockwise, we have;
b·x = 45°, therefore;
h = 105 × cos(45° + 90°) + 0 = 105 × cos(135°) + 0
h = 105 × cos(135°) ≈ -74.25 feet
Therefore, the height of the seat of the Ferris wheel reduces by 74.246 feet.
