The radius of ferris wheel is r = 29 feet.
The equation for the vertical distance is,
[tex]y=r\sin \theta[/tex]For rotation of 3.5 radians,
[tex]\begin{gathered} \theta=3.5\times\frac{180}{\pi} \\ =200.53^{\circ} \end{gathered}[/tex]Determine the vertical distance of Josie.
[tex]\begin{gathered} y=29\cdot\sin 200.53 \\ =29\cdot(-0.3508) \\ =-10.1732 \end{gathered}[/tex]Josie is 10.1732 feet below the horizontal.
Part B:
The distance travelled by Josie is s = 237 feet.
Determine the rotation for distance travelled by Josie.
[tex]\begin{gathered} \theta=\frac{s}{r} \\ =\frac{237}{29} \\ =468.244^{\circ} \end{gathered}[/tex]Determine the vertical distance of Josie.
[tex]\begin{gathered} y=29\cdot\sin (468.244) \\ =29\cdot0.949 \\ =27.54 \end{gathered}[/tex]Josie is 27.544 feet above the horizontal.
Part C:
The function for the vertical distance above the horizontal is,
[tex]f(s)=29\sin (\frac{s}{29})[/tex]Here angle is in radians.