a rope swing is attached to tree overlooking the river. if the rope is 38 feet in length and swings through an angle of 200 degree, find the total distance to the nearest feet, traveled by someone sitting on the seat when the swing angle described is the maximum.
Its 133
mogul
To find the total distance traveled by someone sitting on the seat when the swing angle is at its maximum, we need to calculate the length of the arc traveled by the swing.
The formula to calculate the length of an arc is given by:
Arc Length = r * θ
Where:
- r is the radius (length of the rope in this case)
- θ is the angle in radians
However, the angle given in the problem is in degrees, so we need to convert it to radians by multiplying it by π/180.
Given:
- Length of the rope (r) = 38 feet
- Angle (θ) = 200 degrees
First, let's convert the angle from degrees to radians:
θ (in radians) = θ (in degrees) * π/180
θ (in radians) = 200 * π/180
θ (in radians) = 10π/9
Now, substitute the values into the arc length formula:
Arc Length = r * θ
Arc Length = 38 * 10π/9
To get the total distance traveled, we need to multiply the arc length by 2 because the swing goes back and forth:
Total Distance Traveled = 2 * Arc Length
Total Distance Traveled = 2 * (38 * 10π/9)
Now, let's calculate the total distance traveled:
Total Distance Traveled = 2 * (38 * 10π/9)
Total Distance Traveled ≈ 844 feet (rounded to the nearest foot)
Therefore, the total distance, to the nearest foot, traveled by someone sitting on the swing when the swing angle is at its maximum is approximately 844 feet.