It seems you've uploaded an image containing a mathematical problem related to a ferris wheel and its motion. Based on the provided graph and questions, here’s a detailed response:

Analyzing the Questions:

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

Looking at the graph, the time for one full cycle (peak-to-peak) appears to be 12 minutes.
However, your response is marked with a warning, possibly indicating a calculation or input error.

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

The graph shows the height oscillating between 0m and 80m. The difference gives the diameter:
Diameter = 80m (correct answer).

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

From the graph, the height at $t = 0$ is 40m, which is the midpoint (radius) of the wheel (correct answer).

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

The loading platform is at the lowest point of the ferris wheel, which corresponds to 0m (correct answer).

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

The graph spans 24 minutes, covering two full cycles (0–24 minutes). Your answer may have been marked wrong due to a discrepancy here.

Suggestions for Corrections:

1. (a) Double-check that the period of one rotation is 12 minutes and verify any misinterpretation.
2. (e) For the total ride duration, note that the graph shows two cycles, totaling 24 minutes, not 12 minutes.

Would you like me to elaborate further on any of the parts? Let me know if you’d like a clearer explanation or additional breakdowns.

Related Questions:

1. What is the relationship between the period and frequency of the ferris wheel's motion?
2. How would the graph change if the loading platform were at 5m instead of 0m?
3. Can you derive the equation of motion for the height $h(t)$ as a sinusoidal function of time $t$?
4. What would be the maximum speed of a rider if the ferris wheel's diameter were increased to 100m?
5. How would the graph change if the ferris wheel rotated twice as fast?

Tip:

When analyzing periodic motion from a graph, always check the period by observing the time between identical points on consecutive cycles (e.g., peaks or troughs).