Question

​9.​The original Ferris wheel, built by George Ferris for the Columbian Exposition of 1983, was much larger and slower than its modern counterparts: It had a diameter of 250 feet and contained 36 cars, each of which held 40 people; it made one revolution every 10 minutes. Suppose that the Ferris wheel revolves counterclockwise in the plane with its center at the origin. Car in the figure had coordinates at time . Find the rule of a function that gives the coordinate of car at time

Answer 1

Answer on Question #44665-Physics-Mechanics-Kinematics-Dynamics

The original Ferris wheel, built by George Ferris for the Columbian Exposition of 1893, was much larger and slower than its modern counterparts: it had a diameter of 250 feet and contained 36 cars, each of which held 40 people. It made one revolution every 10 minutes. Suppose that the Ferris wheel revolves counterclockwise in the x-y plane with its center at the origin. Car D in the figure had a coordinates (125, 0) at time $t = 0$ . Find the rule of a function that gives the y-coordinate of car D at time $t$ .

Solution

The most general form of the equation that describes any object undergoing SHM (simple harmonic motion) is given by:

$$y = A \sin (2 \pi f t + \varphi) + B.$$

In our case

$$f = \frac {1}{1 0} r p m = \frac {1}{1 0} \cdot \frac {1}{6 0} H z = \frac {1}{6 0 0} H z$$

$y = 0$ at time $t = 0$ :

$$0 = A \sin (\varphi) \rightarrow \varphi = 0$$ $$A = \frac {2 5 0}{2} = 1 2 5.$$

The rule of a function that gives the y-coordinate of car D at time t

$$y = 1 2 5 \sin (2 \pi \frac {1}{6 0 0} t) = 1 2 5 \sin \left(\frac {\pi t}{3 0 0}\right).$$

Answer: 125 sin $\left(\frac{\pi t}{300}\right)$ .

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