Sheldon notices the Ferris Wheel radius is 40 feet and the center of the wheel is 50 feet high. Amy times the ride and finds it takes 45 seconds to complete one turn around the wheel.

Question

1. At what speed is the platform moving. (in feet per second)?
2. Through what angle (in degrees) does the Ferris wheel turn each second?
3. What is the height of the platform when it is in each of position?(Draw a reference triangle before solving)

a. 3 o'clock

b. 12 o'clock

c. 2 o'clock

d. 4 o'clock

Answer 1

1) Amy traverses the whole circumference, 2πr, in 45 seconds. So, 80π ft / 45 secs ~ 5.6 ft/sec.

2) 360° / 45 secs = 8° / sec

3a) At center height

3b) Center height + radius

3c) Center height + radius · sin30° (Each hour of the clock represents 30° of rotation, since 360° / 12 hrs.)

3d) Center height - radius · sin30°