The relationship between an object's gravitational potential energy (GPE) and its height above the ground (h) is typically linear. The formula for gravitational potential energy is given by:
\[ \text{GPE} = mgh \]
where:
- \( \text{GPE} \) is the gravitational potential energy,
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \) near the Earth's surface),
- \( h \) is the height above the ground.
From this equation, we can see that as the height \( h \) increases, the gravitational potential energy also increases linearly if the mass \( m \) and gravity \( g \) are constant.
Thus, a graph showing this relationship would have height (h) on the x-axis and gravitational potential energy (GPE) on the y-axis, resulting in a straight line that slopes upward. The slope of this line would be equal to \( mg \).
If you have specific graphs to choose from, find the one that depicts a straight line starting from the origin and sloping upwards as height increases. That is the correct representation of the relationship between gravitational potential energy and height.