A tetherball hangs from a rope on a pole. The tetherball is 6 feet away from the pole as it swings around the pole.
As the tetherball swings around the pole, it follows a circular path. The distance between the tetherball and the pole remains constant at 6 feet throughout its swing.
To calculate the path of the tetherball as it swings around the pole, you can use the concept of a circle and the Pythagorean theorem. Here are the steps:
1. Imagine the pole as the center of a circle.
2. The 6 feet distance between the tetherball and the pole represents the length of the rope, which would be the radius of the circle.
3. Now, as the tetherball swings around the pole, it moves along the circumference of this circle.
4. To find the distance traveled by the tetherball, you need to calculate the circumference of the circle.
- The formula to find the circumference (C) of a circle is C = 2πr, where r is the radius.
- Plugging in the given radius of 6 feet, we get C = 2π(6) = 12π feet as the distance traveled by the tetherball per revolution around the pole.
5. Additionally, you may want to know the distance between the starting and ending points of each swing.
- Since the tetherball swings around a full circle, the starting and ending points will be diametrically opposite on the circumference of the circle. Hence, the distance between them is equal to the diameter of the circle.
- The formula to find the diameter (D) of a circle is D = 2r, where r is the radius.
- Plugging in the given radius of 6 feet, we get D = 2(6) = 12 feet as the distance between the starting and ending points of each swing.
So, the tetherball swings around the pole along the circumference of a circle with a radius of 6 feet. The distance traveled per revolution is 12π feet, and the distance between the starting and ending points of each swing is 12 feet.