Preview Activity 2.1.1.
In the context of the ferris wheel pictured in Figure 2.1.1 in the text, assume that the height, \(h\text{,}\) of the moving point (the cab in which you are riding), and the distance, \(d\text{,}\) that the point has traveled around the circumference of the ferris wheel are both measured in meters.
Further, assume that the circumference of the ferris wheel is \(150\) meters. In addition, suppose that after getting in your cab at the lowest point on the wheel, you traverse the full circle several times.
(a)
Recall that the circumference, \(C\text{,}\) of a circle is connected to the circle’s radius, \(r\text{,}\) by the formula \(C = 2\pi r\text{.}\) What is the radius of the ferris wheel? How high is the highest point on the ferris wheel?
(b)
How high is the cab after it has traveled \(1/4\) of the circumference of the circle?
(c)
How much distance along the circle has the cab traversed at the moment it first reaches a height of \(\frac{150}{\pi} \approx 47.75\) meters?
(d)
(e)
(f)
Why do you think the curve shown at right in Figure 2.1.1 has the shape that it does? Write several sentences to explain.
