When a baseball is dropped from a certain height, it falls under the influence of gravity. Assuming no air resistance, the relationship between the final velocity (v_f) of the baseball just before it strikes the ground and the starting height (h) can be described by the physics formula for gravitational potential energy and kinetic energy.
The final velocity can be determined using the equation derived from the conservation of energy or directly from kinematic equations:
\[ v_f = \sqrt{2gh} \]
Where:
- \( v_f \) is the final velocity just before impact,
- \( g \) is the acceleration due to gravity (approximately 9.81 m/s²),
- \( h \) is the height from which the baseball is dropped.
From this relationship, we see that the final velocity is proportional to the square root of the height. This means that if you plot the final velocity against the height, the graph will represent a square root curve.
Specifically, the graph will start at the origin (0,0) and increase, gradually becoming less steep as height increases. This indicates that as the height increases, the final velocity increases, but at a decreasing rate due to the square root relationship.
In summary, the correct graph will depict a curve that begins at the origin and rises, showing that final velocity increases as height increases, specifically following a square root function.
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