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Modeling Circular Motion - 2.6.18

Each graph shows the vertical position , in inches, of a point on the outside of a bike wheel,  seconds after the wheel begins to spin. Which bike has larger wheels? Explain how you know.

Which bike’s wheels are spinning faster? Explain how you know.

Jada, Noah, and Elena are riding a carousel.

Here is a view, from above, of the carousel.

The carousel moves in a counterclockwise direction. When the ride begins, Jada is at position , Noah is at position , and Elena is at position . The measure of angle  is  and the measure of angle  is . The radius of the carousel is 20 feet. How far does Jada travel to reach Noah’s starting position? What about Elena’s starting position? Explain or show how you know.

The carousel makes 1 complete rotation every 10 seconds. At which times will Jada be at her starting position? At which times will she be at Noah's starting position? Explain or show how you know.