The relationship between the final velocity of a dropped baseball just before it strikes the ground and its starting height is characterized by the principles of physics, specifically the equations of motion and conservation of energy.
When a baseball is dropped from a height, its potential energy at the starting height is converted into kinetic energy as it falls. The final velocity just before impact can be calculated using the following equation derived from energy conservation:
\[ v_f = \sqrt{2gh} \]
where:
- \( v_f \) is the final velocity just before striking the ground,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , m/s^2 \)),
- \( h \) is the height from which the baseball is dropped.
This equation indicates that the final velocity is proportional to the square root of the height \( h \). Therefore, if you were to graph this relationship, you would have:
- The x-axis representing the starting height \( h \),
- The y-axis representing the final velocity \( v_f \).
The graph would be a curve that starts at the origin (0,0) and increases, resembling the shape of a square root function. As height increases, the increase in final velocity becomes less pronounced, which reflects the diminishing return of the square root function.
So, the graph that represents this relationship will be a curve that rises quickly at first and then levels off, indicating that as the height increases, the final velocity does too, but at a decreasing rate.
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