Answer :
Answer
Angle of rotation for the merry go round = 121°
Explanation
The distance travelled by the wheel by moving/rotating through an angle is the length of the arc that would subtend the angle moved through at the center of the circle.
[tex]\text{Length of an arc = }\frac{\theta}{360\degree}\times2\pi r[/tex]where
Length of the arc = 38 ft.
θ = Angle that the circular figure moves through = ?
π = pi = 3.14
r = radius of the circle involved in the motion = 18 ft.
[tex]\begin{gathered} \text{Length of an arc = }\frac{\theta}{360\degree}\times2\pi r \\ \text{38 = }\frac{\theta}{360\degree}\times2\pi\times(18) \\ 38=0.3143\theta \end{gathered}[/tex]We can rewrite this as
0.3143θ = 38
Divide both sides by 0.3143
(0.3143θ/0.3143) = (38/0.3143)
θ = 120.9° = 121° to the nearest degree.
Hope this Helps!!!