A girl sitting on a merry-go-round moves counterclockwise through an arc length of 3.75 m.
If the girl’s angular displacement is 2.12 rad, how far is she from the center of the merry-go-round?
Answer in units of m
To find the distance from the center of the merry-go-round, we can use the formula for arc length:
s = rθ
Where:
s = arc length
r = radius of the merry-go-round
θ = angular displacement
We are given that the arc length (s) is 3.75 m and the angular displacement (θ) is 2.12 rad.
We can rearrange the formula to solve for the radius (r):
r = s / θ
Substituting the given values:
r = 3.75 m / 2.12 rad
Calculating this expression:
r ≈ 1.76787 m
Therefore, the girl is approximately 1.76787 meters away from the center of the merry-go-round.