To determine the relationship between a freely falling object's gravitational potential energy (GPE) and its height from the ground, we need to recall that gravitational potential energy is given by the formula:
\[ \text{GPE} = mgh \]
where:
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , m/s^2 \) on Earth),
- \( h \) is the height above the ground.
From this equation, we can see that gravitational potential energy is directly proportional to height. This means that as the height \( h \) increases, the gravitational potential energy \( \text{GPE} \) also increases linearly.
Therefore, the graph that best represents this relationship would show a straight line that rises as height increases. If the height is on the x-axis and GPE is on the y-axis, the graph will be a straight line starting from the origin (0,0) and sloping upwards.
If options were provided, you would look for a linear graph that displays this direct proportionality.