Nancy was about to play the first hole on a mini golf course. She placed her golf ball on the mat in front of her and aimed carefully with her golf club. Then, Nancy gently tapped the ball straight toward the hole. The ball rolled slowly along the flat mat before falling to the bottom of the hole. When was the least gravitational potential energy stored between the golf ball and Earth? Assume that the golf ball's mass did not change. when the ball was farthest from the hole when the ball was rolling slowly on the mat when the ball was at the bottom of the hole

Gravitational potential energy (GPE) near the Earth’s surface is given by the equation: \[ \text{GPE} = mgh \] where: - \( m \) is the mass of the object, - \( g \) is the acceleration due to gravity, and - \( h \) is the height above a reference point. In this scenario: - **When the ball was farthest from the hole:** The ball is at its highest position relative to the hole, so \( h \) is maximum, resulting in maximum GPE. - **When the ball was rolling slowly on the mat:** The height \( h \) is slightly lower than when it was farthest from the hole but still relatively high, so GPE is still significant. - **When the ball was at the bottom of the hole:** The ball is at its lowest position, meaning \( h \) is at its minimum. Therefore, the GPE is the least at this point. **Conclusion:** The least gravitational potential energy was stored when the ball was at the bottom of the hole. **Answer:** when the ball was at the bottom of the hole