Question: The height above the ground of a rider on a ferris wheel can be modeled by the sine function shown below.
How close to the ground does the rider get ?
Graph: a blue sinusoidal wave on a grid in the top-left area; the curve has two peaks and two troughs, oscillating across the graph with the minimum height about 2.5 m above the ground, so the answer is 2.5 m. position_hint \in \{top-left\}.
5 m
17.5 m
15 sec
2.5 m
1. **State the problem:** We want to find how close the rider on the ferris wheel gets to the ground, which means finding the minimum height of the sine function modeling the height.
2. **Recall the sine function properties:** The sine function oscillates between -1 and 1. When modeling height, the function is usually of the form $$h(t) = A \sin(Bt + C) + D$$ where:
- $A$ is the amplitude (height from the midline to peak),
- $D$ is the vertical shift (midline height),
- The minimum height is $D - A$.
3. **Analyze the graph information:** The graph shows the minimum height is about $2.5$ meters above the ground.
4. **Conclusion:** The closest the rider gets to the ground is the minimum height of the sine wave, which is $$\boxed{2.5 \text{ meters}}.$$