To understand the relationship between the final velocity of a dropped object just before it strikes the ground and its starting height, we can use the principles of physics. When an object is dropped from a certain height, it accelerates downward due to gravity. The final velocity can be calculated using the equation derived from conservation of energy and kinematics.
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Kinematic Equation: The key kinematic equation is: \[ v^2 = u^2 + 2gh \] where:
- \(v\) is the final velocity,
- \(u\) is the initial velocity (which is 0 for an object dropped from rest),
- \(g\) is the acceleration due to gravity (approximately \(9.81 , m/s^2\)),
- \(h\) is the height from which it was dropped.
Since the object starts from rest (\(u = 0\)), this simplifies to: \[ v^2 = 2gh \]
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Final Velocity and Starting Height: The final velocity \(v\) before striking the ground is therefore: \[ v = \sqrt{2gh} \] This equation shows that the final velocity \(v\) is directly proportional to the square root of the height \(h\). As the height increases, the final velocity increases as well, but at a decreasing rate (since it's a square root function).
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Graph Representation: The graph that represents this relationship would be a curve starting from the origin (0,0) that rises and flattens out as height increases. This reflects the square root relationship, where velocity increases more quickly at lower heights and then more slowly at higher heights.
Therefore, the best graph to represent the relationship between final velocity and starting height will be a curve that shows a gradual increase, starting from the origin, and approaching a horizontal asymptote as height increases.