Chapter 13.6, Problem 28PPS

To determine

To sketch the graph of the function

Explanation of Solution

Given:

Ferris wheel is 520ft. in diameter. It takes 30 seconds to complete one revolution.

Calculation:

Given that the Ferris wheel is 520ft. in diameter, so any compartment at the periphery of the wheel undergoes periodic motion of amplitude equal to the radius of the wheel.

Amplitude, $A=\frac{520}{2}=260\text{feet}.$

As one complete revolution of the wheel requires $30$ seconds, so the period of circular motion of the wheel is $T=30$ sec.

Hence angular velocity of the wheel will be

  $\omega =\frac{2\pi }{T}=\frac{2\pi }{30}=\frac{\pi }{15}$ .

So the height of a compartment at time $t$ which starts at $t=0$ can be written as a function of $t$ as:

  $h\left(\theta \right)=260\sin \frac{\pi }{15}\theta +260$

Graph:

  

Interpretation:

The above graph is the required graph.