Sheldon and Amy are waiting in line to ride the Ferris Wheel at their local amusement park

Question

Sheldon and Amy are waiting in line to ride the Ferris Wheel at their local amusement park. Sheldon notices the radius of the wheel 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.

1. What is the horizontal location of the platform when it is in each of these positions?

a. 3 o’clock

b. 12 o’clock

c. 2 o’clock

d. 4 o’clock

2. What is the platform’s horizontal location at each of these times?

a. 3 seconds after passing the 3 o’clock position

b. 12 seconds after passing the 3 o’clock position

c. 24 seconds after passing the 3 o’clock position

d. 35 seconds after passing the 3 o’clock position

Answer 1

Horizontal position is cos of the angle through the 3:00 position, running counterclockwise

3:00 is 0°, and 40cos(0°) = 40*1=40 m

12:00 is 90° and 40cos(90°)=0 m

2:00 is 30°, and 40cos(30°)= 40*√3/2 = 20√3≈34 m

4:00 is 330° and 40cos(330°)= 40*√3/2 = 20√3≈34 m

Note that angle above and below the horizontal axis makes no difference to the horizontal distance, as it is symmetrical. Therefore, it doesn't matter which way the wheel is rotation for the rest of the problem.

3 seconds is 1/15 of a rotation so 24°, so 40cos(24°) ≈ 36 m

12 seconds is 4/15 of a rotation, so 96°, so 40cos(96°)≈ -4 m

24 seconds is 8/15 of a rotation, so 192°, so 40cos(192°)≈ -39 m

35 seconds is 7/9 of a rotation, so 280°, so 40cos(248°)≈ 7 m