Let's analyze each question using the information provided from the graph.

(a) How long does it take the ferris wheel to complete one full rotation?

To determine the time for one full rotation, we observe the period of the graph. The graph shows a sinusoidal pattern that starts at a peak, reaches another peak around $t = 6$ minutes. Therefore, one full rotation (the time it takes for the pattern to repeat) takes 6 minutes.

Answer: 6 minutes

(b) What is the diameter of the ferris wheel?

The diameter of the ferris wheel corresponds to the distance between the maximum and minimum heights on the graph. From the graph:

• The maximum height is approximately $h = 100$ meters.
• The minimum height is approximately $h = 10$ meters.

The difference between these heights gives the diameter: $100 - 10 = 90 \text{ meters}$

Answer: 90 meters

(c) What is your height at time $t = 0$?

At $t = 0$, the height $h$ appears to be at the maximum point on the graph, which is 100 meters.

Answer: 100 meters

(d) What is the height of the loading platform?

The loading platform's height is represented by the lowest point on the graph, which is 10 meters.

Answer: 10 meters

(e) What length of time does the graph show you riding the wheel?

The graph shows two complete rotations, with a period of 6 minutes per rotation, so the total time displayed on the graph is: $6 \times 2 = 12 \text{ minutes}$

Answer: 12 minutes

Would you like further explanation or have questions on any part?

Here are some related questions for deeper understanding:

1. How would you determine the maximum height of the ferris wheel if it wasn’t explicitly shown on the graph?
2. How would the graph change if the diameter of the ferris wheel were increased?
3. What would the period be if the ferris wheel rotated faster, completing one full rotation in 4 minutes?
4. How can you determine the center of the ferris wheel from the graph?
5. How would you find your height at a specific time between two points shown?

Tip: For sinusoidal functions, the period is the time taken for one complete cycle, and it can often be determined by identifying two consecutive peaks or troughs on a graph.