Final answer:
The Ferris wheel riders spend approximately 0.93 minutes of the 5-minute ride higher than 35 meters above the ground, calculated by finding the angles at which the wheel is higher than the stated height and then using the proportion of these angles to the full revolution.
Step-by-step explanation:
Given that the Ferris wheel has a diameter of 40 meters, the radius of the wheel is half of that, which is 20 meters. Since the loading platform is 2 meters above the ground, the highest point of the Ferris wheel would be 40 meters above the ground (20 meters radius above the base of the wheel plus the 20 meters radius above the platform).
When we consider the points on the Ferris wheel that are higher than 35 meters above the ground, we are looking for the positions on the wheel where the riders are at least 33 meters above the platform (since the platform itself is 2 meters above the ground). Drawing a vertical line from the center of the wheel to the edge, we see that the angle subtended by this line and the line from the center to the 35-meter height point forms a right-angled triangle.
Using trigonometric relationships, specifically the cosine function (cos(theta) = adjacent/hypotenuse), we can calculate this angle, then use it to find the proportion of the ride spent above 35 meters:
cos(theta) = 33/20, so theta approximately equals 33.6 degrees. Since the wheel is symmetrical, we have this angle on both sides of the highest point. Therefore, the proportion of the full revolution above 35 meters is (33.6 * 2) out of 360 degrees.
Calculating the time spent above 35 meters:
(67.2/360) * 5 minutes = 0.93 minutes. Therefore, riders spend approximately 0.93 minutes higher than 35 meters during the 5-minute ride.