Question

The Carousel at Carowinds has 4 rings of horses. Fred is riding on the inner ring, which has a radius of 7 feet. Juan is riding on the outer ring, which is 10 feet farther out from the center than the inner ring is. In one rotation of the carousel, how much farther does Juan travel than Fred? Use 3.14 for .

Answer 1

Juan travel 31.4 feet farther than Fred in one rotation.

Explanation:

In this problem we need to determine the change in linear position of Fred and Juan, whose formula is:

`s=\theta \cdot r` (Eq. 1)

Where:

`r` - Radius, measured in feet.

`\theta` - Angular arch, measured in radians.

`s` - 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 (
`r = 7\,ft`,
`\theta = 2\pi`)

`s= 2\pi\cdot (7\,ft)`

`s = (3.14)\cdot (7\,ft)`

`s = 21.98\,ft`

Juan (
`r = 17\,ft`,
`\theta = 2\pi`)

`s= 2\pi\cdot (17\,ft)`

`s = (3.14)\cdot (17\,ft)`

`s = 53.38\,ft`

And the difference between both travelled distances is:

`\Delta s = 53.38\,ft-21.98\,ft`

`\Delta s = 31.4\,ft`

Juan travel 31.4 feet farther than Fred in one rotation.