Answer:
Juan travel 31.4 feet farther than Fred in one rotation.
Step-by-step explanation:
In this problem we need to determine the change in linear position of Fred and Juan, whose formula is:
[tex]s=\theta \cdot r[/tex] (Eq. 1)
Where:
[tex]r[/tex] - Radius, measured in feet.
[tex]\theta[/tex] - Angular arch, measured in radians.
[tex]s[/tex] - Change in linear position, measured in feet.
If both makes one rotation in the carousel, we obtain the change in linear position of each player:
Fred ([tex]r = 7\,ft[/tex], [tex]\theta = 2\pi[/tex])
[tex]s= 2\pi\cdot (7\,ft)[/tex]
[tex]s = (3.14)\cdot (7\,ft)[/tex]
[tex]s = 21.98\,ft[/tex]
Juan ([tex]r = 17\,ft[/tex], [tex]\theta = 2\pi[/tex])
[tex]s= 2\pi\cdot (17\,ft)[/tex]
[tex]s = (3.14)\cdot (17\,ft)[/tex]
[tex]s = 53.38\,ft[/tex]
And the difference between both travelled distances is:
[tex]\Delta s = 53.38\,ft-21.98\,ft[/tex]
[tex]\Delta s = 31.4\,ft[/tex]
Juan travel 31.4 feet farther than Fred in one rotation.
