Respuesta :
Answer:
The angle of rotation is 2.11 °
Step-by-step explanation:
Given as :
The radius of the round path = r = 18 feet
The length of the distance cover by wheel = l = 38 feet
Let The angle of rotation = Ф
Now, According to question
∵ length of the arc of a circle subtending an angle at center = Ф
So,
length of the distance cover by wheel = π × radius × [tex]\frac{\Theta }{180^{\circ}}[/tex]
Since 180° = π radian
And π = 3.14
So, length of the distance cover by wheel = 180 °× radius × [tex]\frac{\Theta }{180^{\circ}}[/tex]
i.e l = r × Ф
Or, Ф = [tex]\frac{l}{r}[/tex]
Or, Ф = [tex]\frac{38 feet}{18 feet}[/tex]
Or, Ф = 2.11 °
So, The angle of rotation = Ф = 2.11 °
Hence, The angle of rotation is 2.11 ° Answer
The angle of rotation of the passenger sitting in given sized merry go round is calculated by the fact that the whole rotation makes 360 degrees.
Thus, we have the angle of rotation as 120.96 degrees.
Given that:
- Radius of merry-go-round = 18 feet.
- The passenger covered 38 feet.
Calculations:
The whole circle rotation is 360 degrees. If we make [tex]\theta[/tex] degree rotation, then we reach:
[tex]360 \: \rm degrees = 2\pi r \: \rm distance\\\\1^{\circ} = \dfrac{\pi r }{180} \: \rm distance\\\\\\\theta^{\circ} = \dfrac{\pi r \times \theta}{180} \: \rm distance\\[/tex]
Given distance covered = 38, thus putting in above equation:
[tex]38 \: \rm feet = \dfrac{\pi \times 18 \times \theta}{180}\\\theta = \dfrac{380}{\pi}\\\\\theta = 120.9577.. \: \rm degrees[/tex]
Thus, the angle of rotation for given conditions is 120.96 degrees.
Learn more about angle of rotation here:
https://brainly.com/question/17671314
