Q. 108 - Precalculus Enhanced with Graphing Utilities

Question

A neighborhood carnival has a Ferris wheel whose radius is 30 feet. You measure the time it takes for one revolution to be 70 seconds. What is the linear speed (in feet per second) of this Ferris wheel? What is the angular speed in radians per second? 

Step-by-Step Solution

Answer

The linear speed is 2.69 feet per second.

The angular speed is 0.089 radian per second.

Step 1: Given information

Radius of the ferris wheel $\left(r\right)=30 \mathrm{feet}$

The time it takes for one revolution to be 70 seconds. 

Step 2: Calculate the linear speed and angular speed.

The linear speed is computed by using formula shown below,

$$\begin{gathered} \mathrm{Linear} \mathrm{speed}=\frac{\mathrm{Circumference}}{\mathrm{Time}} \\ \mathrm{Linear} \mathrm{speed}=\frac{2\mathrm{\pi r}}{\mathrm{T}} \\ \mathrm{Linear} \mathrm{speed}=\frac{2\times 3.14\times 30}{70} \\ \mathrm{Linear} \mathrm{speed}=2.69 \mathrm{feet} \mathrm{per} \mathrm{second} \end{gathered}$$

The angular speed is computed as;

$$\begin{gathered} \mathrm{Angular} \mathrm{speed}=\frac{2\mathrm{\pi r}}{\mathrm{T}} \\ \mathrm{Angular} \mathrm{speed}=\frac{\mathrm{One} \mathrm{revolution}}{\mathrm{T}}=\frac{2\mathrm{\pi }}{70} \\ \mathrm{Angular} \mathrm{speed}=\frac{2\times 3.14}{70} \\ \mathrm{Angular} \mathrm{speed}=0.089 \mathrm{radian} \mathrm{per} \mathrm{second} \end{gathered}$$