To determine the relationship between a freely falling object's gravitational potential energy (GPE) and its height from the ground, we can use the formula for gravitational potential energy:
\[ \text{GPE} = m \cdot g \cdot h \]
where:
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity, and
- \( h \) is the height of the object above the ground.
From this formula, we can see that gravitational potential energy is directly proportional to height. As height increases, the gravitational potential energy also increases linearly.
If you are looking at graphs, the graph that best represents this relationship would be a straight line that rises from left to right, indicating that as height increases, gravitational potential energy increases proportionally.
In summary, choose the graph that shows a straight line ascending as height increases to represent the relationship between gravitational potential energy and height for a freely falling object.