To analyze the relationship between gravitational potential energy (GPE) and the height of a freely falling object, we can use the formula for gravitational potential energy:
\[ GPE = mgh \]
where:
- \( GPE \) is the gravitational potential energy,
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)),
- \( h \) is the height above the ground.
From this equation, we can see that the gravitational potential energy is directly proportional to the height (h). When height increases, gravitational potential energy also increases, and when height decreases, gravitational potential energy decreases. This creates a linear relationship between GPE and height.
Thus, the graph that best represents this relationship will be a straight line that slopes upward, showing that as height increases, gravitational potential energy increases correspondingly.
If any of the options (A, B, C, or D) display a graph with a linear relationship where GPE increases as height increases, that would be the correct choice. If they show a curve or any other form of non-linear relationship, those options would not represent the relationship correctly.
Please check the options to identify the one that fits this description!