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 of the girl from the center of the merry-go-round, we can use the relationship between the arc length, the radius, and the angular displacement.
The formula for arc length is given by:
Arc Length = Radius × Angular Displacement
We are given the arc length (3.75 m) and the angular displacement (2.12 rad). Let's represent the radius with the letter 'r'.
Plugging in the values we have, we get:
3.75 m = r × 2.12 rad
To find the radius 'r', we need to rearrange the equation:
r = 3.75 m / 2.12 rad
Calculating this, we get:
r ≈ 1.768 m
Therefore, the girl is approximately 1.768 meters away from the center of the merry-go-round.