ANSWER :
18.8 inches per second
EXPLANATION :
The ferris wheel completes 7 revolutions in 14 minutes.
So we can say that the ferris wheel completes 1 revolution in 14/7 = 2 minutes.
Note that the circumference formula of a circle is :
[tex]C=2\pi r[/tex]
This is the distance travelled in one revolution.
So we need to find the circumference of the circle in inches.
The ferris wheel has a radius of 30 feet.
Convert 30 feet into inches :
[tex]30\cancel{ft}\times\frac{12in}{1\cancel{ft}}=360in[/tex]
Using the formula above :
[tex]\begin{gathered} C=2\pi r \\ C=2\pi(360) \\ C=2261.947in \end{gathered}[/tex]
Now we have the time and the distance travelled.
The velocity is distance divided by the time.
The time is in minutes. So we need to convert it to seconds.
[tex]2\cancel{min}\times\frac{60sec}{1\cancel{min}}=120sec[/tex]
So we have time = 120 secs and the distance is 2261.947 inches
The velocity is :
[tex]\begin{gathered} v=\frac{2261.947}{120} \\ v=18.8\text{ inches per second} \end{gathered}[/tex]
