Solution
Given that;
A ferris wheel completes 7 revolutions in 14 minutes
[tex]\begin{gathered} \Rightarrow1\text{ revolutions }=\frac{14}{7}\text{ minutes = 2 minutes } \\ \\ \Rightarrow1\text{ rev = 2}\times1\text{ minutes}=2\times60\text{ sec} \\ \\ \Rightarrow1\text{ rev }=120\text{ sec} \\ \\ \Rightarrow\text{ angular velocity }\omega=\frac{1}{120}\frac{rev}{sec}\times(2\pi\frac{\text{ rad}}{rev}) \\ \\ \Rightarrow\omega=\frac{\pi}{60}\text{ rad/sec} \\ \end{gathered}[/tex]
Given that radius is 30 feet;
30 feet = 360 inches
linear velocity = angular velocity × radius of rotation
[tex]\begin{gathered} \Rightarrow v=\omega r \\ \\ \Rightarrow v=\frac{\pi}{60}\frac{rad}{sec}\times360\text{ inches}=18.8\text{ inches/sec} \end{gathered}[/tex]
Hence, the linear velocity is 18.8 inches/sec
