https://file.aiquickdraw.com/mathbot/file/17254860357351q1xfpwa.jpg

The image appears to contain a math problem involving a geometric figure, possibly a circle or a sector of a circle. It seems to include some multiple-choice options and a labeled diagram. To help you fully, I'll first extract the content from the image and break down the problem and solution.

Let me begin by reviewing the image closely and interpreting the problem details.From the image, I extracted the following information regarding the problem:

### Problem Description:
Two objects, Object 1 and Object 2, move in circular paths. The diagram represents the circular movement of both objects, with Object 2 traveling on a smaller inner circle and Object 1 traveling on a larger outer circle. The angle of the sector of the circle given is \( 60^\circ \).

The problem is to compare the distances (arcs) traveled by each object based on their respective paths.

- **Given**: Angle of the sector \( = 60^\circ \)
- **Assumed (from the diagram)**: The radii of the circles seem to be proportional, but the exact radii are not explicitly given.

### Options:
1. **Object 1 travels farther than Object 2.**
2. **Object 2 travels farther than Object 1.**
3. **Both travel the same distance.**
4. **More information is required.**

### To Solve:
The arc length \( s \) for an object traveling along a circular path is given by:
\[
s = r \theta
\]
where \( r \) is the radius of the circle, and \( \theta \) is the angle subtended by the arc at the center of the circle (in radians).

Since the angle is the same for both objects (both subtend \( 60^\circ \)), the arc length depends on the radius. Object 1, moving along the larger circle, will travel a greater distance than Object 2, as the arc length is proportional to the radius.

Thus, the correct answer is likely:

**Object 1 travels farther than Object 2.**

Would you like a more detailed explanation of the arc length calculation? 

Here are 5 related questions to expand your understanding:
1. How do you convert degrees to radians?
2. What is the formula for the circumference of a circle?
3. How does the radius affect the arc length of a circle?
4. Can you derive the arc length formula from the circumference formula?
5. What happens to the arc length when the angle is doubled?

**Tip**: When solving circular motion problems, always remember that the arc length depends on both the radius and the angle subtended at the center.

Two objects, Object 1 and Object 2, move in circular paths. The diagram represents the circular movement of both objects, with Object 2 traveling on a smaller inner circle and Object 1 traveling on a larger outer circle. The angle of the sector of the circle given is 60°. The question asks to compare the distances (arcs) traveled by each object based on their respective paths.

This problem involves comparing the arc lengths traveled by two objects moving in circular paths. With a given angle of 60° and different radii for the paths, the problem demonstrates the relationship between arc length and radius. Suitable for students in Grades 9-12.

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