Final answer:
By calculating the angle for which the height of the Ferris wheel exceeds 16 meters and considering the total rotation time, we find that a rider spends approximately 2.16 minutes above 16 meters.
Step-by-step explanation:
To determine how many minutes of the ride are spent higher than 16 meters above the ground, we first need to consider the dimensions and motion of the Ferris wheel. The Ferris wheel has a diameter of 23 meters, which means its radius is 11.5 meters (half of the diameter).
The platform is 3 meters above the ground, and at the six o'clock position, the bottom of the wheel is level with the platform.
Thus, when at the six o'clock position, a rider is 3 meters above the ground.
The highest point a rider can reach is then 3 meters (platform height) plus 23 meters (diameter of the Ferris wheel), totaling 26 meters.
The next step is to calculate the angle relative to the vertical where the height exceeds 16 meters.
Since the rider starts at a height of 3 meters, the vertical distance to reach 16 meters is 16 - 3 = 13 meters.
Using the radius of the Ferris wheel (11.5 meters), we can use trigonometry to find the angle θ such that cos(θ) = 13/11.5. This yields θ ≈ 48.59°.
Because the Ferris wheel is symmetrical, the same angle applies to both the ascending and descending sides of the ride. This gives a total angle of 2 * 48.59° = 97.18° where the rider is above 16 meters.
Finally, since the Ferris wheel completes a full revolution (360°) in 8 minutes, the proportion of time spent above 16 meters is 97.18°/360°.
Calculating this gives (97.18/360) * 8 minutes ≈ 2.16 minutes.
Therefore, the rider spends approximately 2.16 minutes above 16 meters during the ride.