A girl sitting on a merry-go-round 1.50 m from the center moves counterclockwise. If the girl's angular displacement is 1.67 rad, what is the arc length through which she moved?
To calculate the arc length through which the girl moved on the merry-go-round, we can use the formula:
Arc length = radius × angle
Given:
- Radius (r) of the merry-go-round = 1.50 m
- Angular displacement (θ) of the girl = 1.67 rad
Plugging these values into the formula, we have:
Arc length = 1.50 m × 1.67 rad
Calculating the result:
Arc length = 2.505 m
Therefore, the girl moved through an arc length of 2.505 meters.
To determine the arc length through which the girl moved, we need to use the formula:
Arc length (s) = Radius (r) x Angular displacement (θ)
In this case, the radius is given as 1.50 m and the angular displacement is given as 1.67 rad.
Substituting the values into the formula, we get:
Arc length (s) = 1.50 m x 1.67 rad
To calculate this, simply multiply the radius by the angular displacement:
Arc length (s) ≈ 2.5 m
Therefore, the arc length through which the girl moved is approximately 2.5 meters.