Which graph represents the relationship between final velocity of a dropped baseball before striking the ground and the starting height of the baseball
Without specific data points, it is difficult to provide an exact graph. However, the relationship between the final velocity of a dropped baseball before striking the ground and the starting height of the baseball can generally be represented by a simple linear graph.
The graph would be a straight line with a negative slope, indicating that as the starting height of the baseball increases, the final velocity decreases. This relationship is due to the influence of gravity on the motion of the baseball.
As the baseball is dropped from higher and higher heights, it has more potential energy which is converted into kinetic energy as it accelerates downwards. However, due to the effect of air resistance, the acceleration is not constant, hence the graph may not be perfect.
The graph might look something like this:
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h_i (Starting Height)
The relationship between the final velocity of a dropped baseball and its starting height can be represented by a linear graph.
As the ball falls, it accelerates due to the force of gravity. The initial velocity is zero, and the acceleration is constant. Therefore, the final velocity of the ball before striking the ground depends on the starting height.
If we assume that air resistance is negligible, we can use the equation to describe the motion of the ball:
v^2 = u^2 + 2as
Where:
v = final velocity
u = initial velocity (in this case, 0 m/s)
a = acceleration due to gravity (approximately -9.8 m/s^2)
s = vertical distance traveled (starting height)
Rearranging the equation, we get:
v^2 = 2as
Taking the square root of both sides, we have:
v = √(2as)
This equation shows that the final velocity is directly proportional to the square root of the starting height. Therefore, the graph representing the relationship between the final velocity and the starting height of a dropped baseball will be a straight line starting from the origin.
The graph will have the starting height (s) on the x-axis and the final velocity (v) on the y-axis.
To determine which graph represents the relationship between the final velocity of a dropped baseball and the starting height, we need to understand the factors that affect these variables.
When a baseball is dropped, its final velocity before striking the ground depends on its starting height. The higher the starting height, the more time it has to accelerate due to the force of gravity. Therefore, we can conclude that the two variables are related.
To figure out the type of relationship between these variables, we can apply some logical reasoning and background knowledge. As the starting height increases, the baseball has more potential energy, which is converted into kinetic energy as it falls. This kinetic energy is directly proportional to the square of the velocity, according to the kinetic energy equation. So, we can infer that the final velocity of the baseball is directly related to the square root of the starting height.
With this information, let's consider the possible graphs that represent this relationship:
1. Linear Relationship: If the relationship between the final velocity and the starting height were linear, the graph would be a straight line. However, based on our reasoning, we know that the relationship is not linear, so we can eliminate this option.
2. Quadratic Relationship: Since the velocity is directly related to the square root of the starting height, the graph would likely be a curve. Specifically, it would be a concave-upward curve. Therefore, we can conclude that the graph representing this relationship is a quadratic curve.
In summary, the graph representing the relationship between the final velocity of a dropped baseball before striking the ground and the starting height is a concave-upward quadratic curve.