The relationship between a freely falling object's gravitational potential energy (GPE) and its height from the ground can be described using the formula:
\[ \text{GPE} = mgh \]
where:
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \) near the Earth's surface), and
- \( h \) is the height of the object above the ground.
From this equation, we can see that Gravitational Potential Energy is directly proportional to the height \( h \). This means that as the height increases, the gravitational potential energy also increases linearly.
Therefore, the graph that best represents this relationship would be a straight line that starts at the origin (0,0) and rises upward as height increases. The slope of this line would correspond to the product of the mass \( m \) and the acceleration due to gravity \( g \).
If you have options for graphs, look for a linear graph with an upward slope when plotting gravitational potential energy on the y-axis and height on the x-axis.
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