A child swings on a playground swing set. If the length of the rope on the swing is 3m and the child swings through an angle of 0.5 radians, what is the exact arc length that the child travels while swinging?
To find the exact arc length that the child travels while swinging, we can use the formula for the arc length of a circle sector. The formula is given by:
Arc Length = r * θ
Where:
- r is the radius of the circle
- θ is the angle subtended by the arc in radians
In this case, the length of the rope on the swing is the radius of the circle, which is 3m. The child swings through an angle of 0.5 radians.
Substituting these values into the formula, we have:
Arc Length = 3m * 0.5 radians
Now, we can calculate the arc length:
Arc Length = 1.5 meters
So, the exact arc length that the child travels while swinging is 1.5 meters.