Since the text you provided doesn't include the actual graphs or images, I can't tell you which one best represents the relationship between the final velocity of a dropped object and the starting height of the object. However, I can explain the relationship so that might help you figure out which graph is the correct one.
The relationship between the final velocity of a dropped object and its starting height is determined by the laws of physics, specifically by the law of conservation of energy and the equations for gravitational acceleration.
The final velocity \( v \) of an object dropped from a height \( h \) in the absence of air resistance is given by the equation derived from conservation of kinetic and potential energies:
\[ v = \sqrt{2gh} \]
where:
- \( v \) is the final velocity just before striking the ground,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, m/s^2 \) on Earth),
- \( h \) is the starting height from which the object is dropped.
This equation shows that the final velocity is proportional to the square root of the starting height. If you were to graph this relationship, the graph should show that as the height increases, the final velocity increases at a rate that slows down for higher heights. This would be a curve that starts steep and gradually becomes flatter as height increases -- specifically, a square root curve.
Given this information, you should choose the graph that most closely matches a square root function for the relationship between the final velocity and the starting height.
Question 10 (1 point)
Which of the graphs best represents the relationship between the final velocity of a dropped object, before striking the ground, and the starting height of the object?
a
b
c
d
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