Question

At one time, Maple Leaf Village (which no longer exists) had North America’s largest Ferris wheel. The Ferris wheel had a diameter of 56 m, and one revolution took 2.5 min to complete. Riders could see Niagara Falls if they were higher than 50 m above the ground. Sketch three cycles of a graph that represents the height of a rider above the ground, as a function of time, if the rider gets on at a height of 0.5 m at Then determine the time intervals when the rider could see Niagara Falls.

Answer 1

To sketch a graph for the Ferris wheel's height as a function of time, one would create a sine wave with a 156 m amplitude and a 2.5 min period. The time intervals for viewing Niagara Falls can be determined by calculating when the height exceeds 50 m.

Step-by-step explanation:

The task is to sketch a graph that represents the height of a rider above the ground as a function of time on a Ferris wheel with a diameter of 56 m and determine the time intervals during which the rider can see Niagara Falls. Assuming the rider gets on at the lowest point (0.5 m above the ground), the graph will resemble a sine wave starting at 0.5 m, peaking at 56 m minus the radius, and repeating every 2.5 minutes (150 seconds) for three cycles.

To see Niagara Falls, the rider must be above 50 m. Given the wheel's diameter, the radius is 28 m, thus the maximum height achieved is 55.5 m. Therefore, the rider surpasses the 50 m threshold as they reach about 14 m from the top or bottom in their cycle. Calculating the exact time intervals requires finding when the sine wave representing the height exceeds the 50 m marker.