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Radek · Answer 1 · 2023-03-02T04:28:28+0000

Solution

Given that;

A ferris wheel completes 7 revolutions in 14 minutes

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

Given that radius is 30 feet;

30 feet = 360 inches

linear speed = angular speed x radius of the rotation

$\begin{gathered} \Rightarrow v=\omega r \\ \\ \Rightarrow v=\frac{\pi\text{ radian}}{60}*360\text{ inches/sec}=18.8\text{ inches/sec} \end{gathered}$

Therefore, linear velocity is 18.8 inches/sec

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