Let's break this down systematically.

1. Amplitude

The amplitude is half the diameter of the ferris wheel, which tells us the distance from the midline to the peak or trough of the wheel's motion.

• Diameter = 10 meters
• Amplitude $A$ = $\frac{10}{2} = 5$ meters

Answer: Amplitude = 5 meters

---

2. Midline

The midline represents the average height of the motion, which corresponds to the center of the ferris wheel plus the height of the boarding platform.

• The wheel’s center is 5 meters above the platform (half of the diameter).
• The platform is 3 meters above the ground.

Thus, the midline is:
$y = 5 + 3 = 8 \, \text{meters}$

Answer: Midline = y = 8 meters

---

3. Period

The period is the time it takes to complete one full revolution of the ferris wheel. In this case, we are told that the wheel completes one revolution every 2 minutes.

Answer: Period = 2 minutes

---

4. Height after 1 minute

We now need to determine the height above the ground after 1 minute. Since the wheel completes 1 full revolution in 2 minutes, after 1 minute you will be at the topmost point of the ferris wheel (halfway through the revolution).

• The amplitude is 5 meters, so the peak is 5 meters above the midline.
• Since the midline is at 8 meters, the height at the top is:
  $8 + 5 = 13 \, \text{meters}$

Answer: Height after 1 minute = 13 meters

---

Summary of Answers

1. Amplitude: 5 meters
2. Midline: $y = 8$ meters
3. Period: 2 minutes
4. Height after 1 minute: 13 meters

---

Would you like me to derive the full height function $h = f(t)$ for this motion?

---

Here are five follow-up questions to deepen your understanding:

1. How would the function change if the ferris wheel completed a revolution in 3 minutes instead?
2. What would be your height at 0.5 minutes (30 seconds)?
3. Can you express the height as a trigonometric function (sine or cosine)?
4. If the platform height were increased to 5 meters, how would that affect the midline?
5. What is the phase shift if the 6 o'clock position no longer corresponds to the starting point?

Tip: When modeling with sine or cosine, always think about the amplitude, midline, period, and phase shift to get the full equation.