Question

I need helpThis practice is giving me a rough time to solve step by step

Answer 1

Given that;

A ferris wheel completes 7 revolutions in 14 minutes

`\begin{gathered} \Rightarrow1\text{ revolutions }=(14)/(7)\text{ minutes = 2 minutes } \\ \\ \Rightarrow1\text{ rev = 2}*1\text{ minutes}=2*60\text{ sec} \\ \\ \Rightarrow1\text{ rev }=120\text{ sec} \\ \\ \Rightarrow\text{ angular velocity }\omega=(1)/(120)(rev)/(sec)*(2\pi\frac{\text{ rad}}{rev}) \\ \\ \Rightarrow\omega=(\pi)/(60)\text{ rad/sec} \\ \end{gathered}`

Given that radius is 30 feet;

30 feet = 360 inches

linear velocity = angular velocity × radius of rotation

`\begin{gathered} \Rightarrow v=\omega r \\ \\ \Rightarrow v=(\pi)/(60)(rad)/(sec)*360\text{ inches}=18.8\text{ inches/sec} \end{gathered}`

Hence, the linear velocity is 18.8 inches/sec