Question
Which line graph best shows the relationship between the final velocity of a dropped object (before it hits the ground) and the height from which it is dropped?(1 point)
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Answers
GPT-4o mini
The relationship between the final velocity of a dropped object (just before impact) and the height from which it is dropped typically follows the principles of physics related to free fall. As an object falls from a greater height, it accelerates due to gravity, resulting in a higher final velocity just before it hits the ground.
This relationship is generally quadratic. Specifically, the final velocity (v) can be calculated using the equation derived from the conservation of energy or kinematics:
\[ v = \sqrt{2gh} \]
where \( g \) is the acceleration due to gravity and \( h \) is the height.
Based on this, a line graph that shows the relationship between final velocity and height should show a curve upward (specifically, a square root curve) rather than a straight line.
If you have specific options for line graphs, the one that curves upward as height increases would be the best representation of this relationship.
This relationship is generally quadratic. Specifically, the final velocity (v) can be calculated using the equation derived from the conservation of energy or kinematics:
\[ v = \sqrt{2gh} \]
where \( g \) is the acceleration due to gravity and \( h \) is the height.
Based on this, a line graph that shows the relationship between final velocity and height should show a curve upward (specifically, a square root curve) rather than a straight line.
If you have specific options for line graphs, the one that curves upward as height increases would be the best representation of this relationship.