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The image shows a ball rolling down from point A to point D and then continuing up the hill to point G. The task asks which statement best explains the relationship between kinetic energy (KE) and potential energy (PE) as the ball moves along this path.

Let's break down the situation:
- At **point A**, the ball is at a height, so it has **maximum potential energy** (PE) and **minimum kinetic energy** (KE), since it's just starting.
- As the ball rolls downhill to **point D** (the lowest point), its PE decreases and its KE increases because it's gaining speed while losing height.
- At **point D**, the ball has **maximum KE** and **minimum PE** since it's at the lowest point.
- As the ball rolls back uphill from **point D to point G**, its KE decreases (losing speed) and its PE increases (gaining height).
- At **point G**, the ball will again have **maximum PE** and **minimum KE**.

Given this, the correct answer is **option A**:
> A. The kinetic energy of the ball decreases as the ball rolls down the hill to point D, while potential energy increases from point A to point D. As the ball rolls back up the hill to point G, potential energy decreases while kinetic energy increases.

Would you like to dive into more details or ask any questions about this explanation?

Here are 5 related questions to deepen understanding:
1. How does the total mechanical energy of the ball (PE + KE) remain constant if there's no friction?
2. What factors affect the maximum speed of the ball at point D?
3. How would the relationship between KE and PE change if the hill had a different shape?
4. Can you describe how the energy transformation would differ if the ball were rolling up a frictionless surface?
5. How does gravity influence the changes in kinetic and potential energy as the ball moves?

**Tip:** Kinetic energy depends on velocity (\( KE = \frac{1}{2} mv^2 \)), while potential energy depends on height (\( PE = mgh \)), so understanding these formulas helps explain energy changes in various systems.

Which statement BEST explains the relationship between kinetic and potential energy of the ball as it rolls from point A to point D and then to point G?

Analyze the relationship between kinetic energy and potential energy in a rolling ball as it moves from point A to point D and then to point G. This problem explains key concepts like the conservation of mechanical energy, kinetic energy formula, and potential energy formula. Suitable for high school students.

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