Ferris Wheel Motion and Geometry

The video tutorial explains how to model the height of a Ferris wheel rider over time using a cosine function. It starts by describing the Ferris wheel's dimensions and rotation period, then diagrams the wheel to identify key points. The tutorial plots these points on a graph and derives the cosine equation representing the rider's height. It calculates the rider's height at specific times and solves for times when the rider reaches a certain height, using trigonometric concepts and the unit circle.

What is the diameter of the Ferris wheel described in the problem?

• 32 meters

• 17 meters

• 30 meters

• 15 meters

At what height above the ground is the center of the Ferris wheel?

• 32 meters

• 15 meters

• 17 meters

• 2 meters

What is the height of the Ferris wheel at its lowest point?

• 0 meters

• 15 meters

• 17 meters

• 2 meters

What is the maximum height reached by the Ferris wheel?

• 15 meters

• 17 meters

• 32 meters

• 30 meters

What is the amplitude of the cosine function modeling the Ferris wheel's motion?

• 15

• 17

• 32

• 30

What is the period of the cosine function for the Ferris wheel?

• 30 seconds

• 45 seconds

• 60 seconds

• 90 seconds

What is the height of the rider at 45 seconds?

• 15 meters

• 32 meters

• 2 meters

• 17 meters

At what time is the rider first at a height of 15 meters?

• 46.3 seconds

• 45 seconds

• 30 seconds

• 13.7 seconds

At what time is the rider again at a height of 15 meters?

• 45 seconds

• 13.7 seconds

• 46.3 seconds

• 30 seconds

Which quadrant of the unit circle is used to find the second angle for the height of 15 meters?

• First

• Second

• Third

• Fourth