Question

While riding on a carousel that is rotating clockwise, a child travels through an arc length of 15.5 m. If the child’s angular displacement is 3.5 rad. What is the radius of the carousel?

Answer 1

The radius of the carousel can be determined using the formula for arc length S = rθ. With an arc length of 15.5 m and an angular displacement of 3.5 rad, the radius is approximately 4.43 m.

Step-by-step explanation:

To find the radius of the carousel, we can use the formula for arc length in a circle, which connects arc length (S), radius (r), and angular displacement (θ):

S = r θ

We are given the arc length (S = 15.5 m) and angular displacement (θ = 3.5 rad), so we can rearrange the formula to solve for the radius (r):

r = S /θ

By substituting the values we have:

r = 15.5 m / 3.5 rad ≈ 4.43 m

Therefore, the radius of the carousel is approximately 4.43 meters.