1. **State the problem:** We are given the height function of a person on a Ferris wheel as $$h(t) = 20 \sin\left(\frac{\pi}{30}t - \frac{\pi}{2}\right) + 22$$ where $t$ is time in seconds. We need to find the maximum and minimum height of the person above ground level. 2. **Understand the function:** The function is sinusoidal with amplitude 20, vertical shift 22, and a phase shift of $-\frac{\pi}{2}$. The amplitude tells us how far the height varies above and below the midline (vertical shift). 3. **Maximum height:** The sine function ranges from $-1$ to $1$. The maximum value of $\sin(\theta)$ is 1. So, $$\max h(t) = 20 \times 1 + 22 = 20 + 22 = 42$$ 4. **Minimum height:** The minimum value of $\sin(\theta)$ is $-1$. So, $$\min h(t) = 20 \times (-1) + 22 = -20 + 22 = 2$$ 5. **Interpretation:** The person’s height above ground varies between 2 metres (lowest point) and 42 metres (highest point) as the Ferris wheel rotates. **Final answer:** - Maximum height = 42 metres - Minimum height = 2 metres