To determine which line graph best shows the relationship between the final velocity of a dropped object and the height from which it is dropped, we can recall the physics principles involved.
When an object is dropped from a height, it accelerates due to gravity. The final velocity of the object just before it hits the ground can be calculated using the equation from kinematics:
\[ v = \sqrt{2gh} \]
where \( v \) is the final velocity, \( g \) is the acceleration due to gravity (approximately \( 9.81 , m/s^2 \)), and \( h \) is the height from which the object is dropped.
From this equation, we can infer the following:
- The final velocity \( v \) is proportional to the square root of the height \( h \).
- As the height increases, the final velocity increases.
- This relationship indicates that the graph will show a curve that rises more steeply as height increases, but it will not be a linear relationship; it will be a square root curve.
When looking at the graphs provided, you should look for one that:
- Starts at the origin (0,0) because if the height is zero, the final velocity should also be zero.
- Increases, but at a decreasing rate (i.e., it starts steep and flattens out).
If you can provide the options, I could help you determine which graph best represents this relationship.
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