Suppose a Ferris wheel has a radius of 50 feet. We will measure the height of a passenger car that starts in the 3 o’clock position with respect to the horizontal line through the center of the wheel. That is, we consider the height of the passenger car at the outset of the problem (that is, after a 0° rotation) to be 0 feet.
a. Mark the diagram to show the position of a passenger car at 30-degree intervals as it rotates counterclockwise around the Ferris wheel.
b. Sketch the graph of the height function of the passenger car for one turn of the wheel. Provide appropriate labels on the axes
c. Explain how you can identify the radius of the wheel from the graph in part (b).
d. If the center of the wheel is 55 feet above the ground, how high is the passenger car above the ground when it is at the top of the wheel?
Exploratory Challenge: The Paper Plate Model, Revisited
Use a paper plate mounted on a sheet of paper to model a Ferris wheel, where the lower edge of the paper represents the ground. Use a ruler and protractor to measure the height and co-height of a Ferris wheel car at various amounts of rotation, measured with respect to the horizontal and vertical lines through the center of the wheel. Suppose that your friends board the Ferris wheel near the end of the boarding period, and the ride begins when their car is in the three o’clock position as shown.
a. Mark horizontal and vertical lines through the center of the wheel on the card stock behind the plate as shown. We will measure the height and co-height as the displacement from the horizontal and vertical lines through the center of the plate.
b. Using the physical model you created with your group, record your measurements in the table, and then graph each of the two sets of ordered pairs (rotation angle, height) and (rotation angle, co-height) on separate coordinate grids. Provide appropriate labels on the axes.
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