A merry go round has a radius of 3.5 meters. How far does a child standing at the edge travel (path length) if the wheel is rotated 13.0 radians?
To find the distance traveled by a child standing at the edge of the merry-go-round, we need to calculate the circumference of the circle created by the child's path.
We know that the radius of the merry-go-round is 3.5 meters. The circumference of a circle can be found using the formula:
Circumference = 2 * π * Radius
Plugging in the given radius value, we get:
Circumference = 2 * π * 3.5
Now, we need to multiply the circumference by the angle in radians that the wheel is rotated. The formula for calculating the distance traveled along a circular path is:
Distance = Circumference * Angle
Substituting the values we have, we get:
Distance = (2 * π * 3.5) * 13.0
Calculating this:
Distance = 90.605 meters
Therefore, the child standing at the edge of the merry-go-round travels approximately 90.605 meters.