Ferris Wheel Motion Quiz

The video tutorial explains a problem involving Jacob and Emily riding a ferris wheel with a 16-meter diameter at a carnival in Billings, Montana. The instructor derives an equation for their height above the ground as a sinusoidal function of time, considering the wheel's rotation speed of 3 revolutions per minute. The process involves calculating the wheel's radius, understanding the relationship between revolutions and angles, and using trigonometry to express height as a function of time.

What is the radius of the Ferris wheel if its diameter is 16 meters?

• 4 meters

• 8 meters

• 16 meters

• 32 meters

At what height above the ground is the lowest point of the Ferris wheel?

• 0 meters

• 16 meters

• 1 meter

• 8 meters

How many revolutions per minute does the Ferris wheel make?

• 4 revolutions

• 1 revolution

• 3 revolutions

• 2 revolutions

How many seconds does it take for the Ferris wheel to complete one revolution?

• 30 seconds

• 20 seconds

• 40 seconds

• 10 seconds

What is the angular speed of the Ferris wheel in degrees per second?

• 12 degrees

• 21 degrees

• 18 degrees

• 15 degrees

Which trigonometric function is used to calculate the height of Jacob and Emily above the ground?

• Sine

• Tangent

• Cosecant

• Cosine

What is the hypotenuse in the triangle used to calculate the height of Jacob and Emily?

• 1 meter

• 8 meters

• 9 meters

• 16 meters

What is the adjacent side in the triangle used to calculate the height of Jacob and Emily?

• h

• 9 - h

• 8

• 18t

What is the final expression for the height h as a function of time t?

• h = 8 - 9 cos(18t)

• h = 9 - 8 cos(18t)

• h = 9 - 8 sin(18t)

• h = 8 + 9 cos(18t)

What is the maximum height Jacob and Emily can reach on the Ferris wheel?

• 17 meters

• 16 meters

• 9 meters

• 8 meters