The largest Ferris Wheel in the world is the London Eye in England. The height (in metres) of a rider on the London Eye after t minutes can be described by the function h(t) = 67 sin[0.2094(t-30)] + 70

Using this equation i'm supposed to find the diameter, the maximum (top of the wheel), minimum and time it takes for the ferris wheel to go through the motion but I have no idea how to get any of this information using only an equation.

Can someone please help me?

e=mc^2

To find the diameter, maximum height, minimum height, and time it takes for the Ferris wheel to complete one full motion, we can analyze the given equation.

The equation represents the height of a rider on the London Eye at any given time (t) in minutes. Let's break down the equation:

h(t) = 67sin[0.2094(t-30)] + 70

The general form of the equation is h(t) = A sin(B(t-C)) + D, where:
- A represents the amplitude of the function, which is the maximum displacement of the rider from the mean position (midpoint between the highest and lowest points).
- B determines the period of the function, representing the time it takes for the wheel to complete one full cycle.
- C is a phase shift, indicating the time when the Ferris wheel begins its motion.
- D is the vertical shift, indicating the midpoint height of the rider on the Ferris wheel.

From the given equation, we can extract the information needed:

1. Diameter:
The diameter of the Ferris wheel is twice the amplitude of the function. In this case, the amplitude (A) is 67, so the diameter would be 2 * 67 = 134 meters.

2. Maximum Height:
The maximum height can be found by adding the amplitude (A) to the vertical shift (D). In this case, the maximum height would be 67 + 70 = 137 meters.

3. Minimum Height:
The minimum height can be found by subtracting the amplitude (A) from the vertical shift (D). In this case, the minimum height would be 70 - 67 = 3 meters.

4. Time for One Full Motion:
The period (T) of the function can be calculated using the formula T = 2π/B. In this case, B = 0.2094. Therefore, T = 2π/0.2094 ≈ 30.02 minutes. Thus, it takes approximately 30.02 minutes for the Ferris wheel to complete one full motion.

To summarize,
- Diameter = 134 meters
- Maximum Height = 137 meters
- Minimum Height = 3 meters
- Time for One Full Motion = 30.02 minutes