Question

Need help solving this step by step Not sure of the subject of mathematics however, if you can identify this and let me now as well :)

Answer 1

Solution

Given that;

A ferris wheel completes 7 revolutions in 14 minutes

$\begin{gathered} \Rightarrow1\text{ revolution }=\frac{14}{7}\text{ minutes} \\ \\ \Rightarrow1\text{ revolution }=2\text{ minutes} \\ \\ \Rightarrow1\text{ revolutions }=2\times1\text{ minutes} \\ \\ \operatorname{\Rightarrow}1\text{ revolut}\imaginaryI\text{ons}=2\times60\text{ seconds} \\ \\ \Rightarrow1\text{ revolut}\mathrm{i}\text{ons}=120\text{ seconds} \\ \\ \Rightarrow\omega=\frac{1}{120}\text{ rev/sec}\times(2\text{ }\pi\frac{\text{ radians}}{1\text{ rev}}) \\ \\ \Rightarrow\omega=\frac{\pi}{60}\frac{radians}{sec} \end{gathered}$

Given that radius is 30 feet;

30 feet = 360 inches

linear speed = angular speed x radius of the rotation

$\begin{gathered} \Rightarrow v=\omega r \\ \\ \Rightarrow v=\frac{\pi\text{ radian}}{60}\times360\text{ inches/sec}=18.8\text{ inches/sec} \end{gathered}$

Therefore, linear velocity is 18.8 inches/sec