Question

10. Many large cities are building or have built mega Ferris wheels. One is 600 feet in diameter and has 48 cars each seating up to 20 people.

Each time the Ferris wheel turns theta degrees, a car is in a position to load.
a. How far does a car move with each rotation of theta degrees (round to the nearest whole number)?
b. What is the value of theta in degrees?

Answer 1

a) 39 ft

b) 7.5°

Explanation:

Data provided in the question:

Diameter of the Ferris wheel = 600 feet

Thus,

Radius of the Ferris wheel = [ 600 ÷ 2 ] feet = 300 feet

Number of cars = 48

Therefore,

angle between consecutive cars, theta = 2π ÷ 48 radians

a) Distance moved with each rotation of theta degrees

= R × theta

= 300 × [ 2π ÷ 48 ]

= 39.27 ≈ 39 ft

b) 1 radians = [180° ÷ π]

Therefore,

theta = [ 2π ÷ 48 ] × [180° ÷ π]

= 7.5°