why is this a poor model for hitting a baseball?
y = -0.002x^2 + 0.879x + 3.981
I know it gets hit at approx. 4 feet high. The -a gives the right shape like a hill. There's a -4.48 and 443.95 zero, which can be hit for distance. The max is (219.75, 100) so that seems doable. What am i missing?
**** i have to explain why it's not a good example. Another problem had an initial height that was negative and another problem had a vertex y value that couldn't possibly be hit. So what am I missing that makes this equation a poor model of a hitting siutation?
I do not see anything wrong with that parabola.
The equation y = -0.002x^2 + 0.879x + 3.981 represents the height of a baseball after it has been hit, where y is the height in feet and x is the horizontal distance the ball has traveled in feet. While the equation may seem reasonable initially, there are a few reasons why it might not be a good model for hitting a baseball.
1. Vertical displacement: In this equation, the highest point of the ball's trajectory, also known as the vertex, is at (219.75, 100). This means that at a horizontal distance of 219.75 feet, the ball reaches a height of 100 feet. In reality, it is highly unlikely for a baseball to be hit that high. Therefore, the vertex value does not align with typical hitting situations, making this equation an inaccurate model.
2. Negative initial height: Another issue with this equation is that it does not account for the initial height from which the ball is hit. In real-world scenarios, a baseball is typically hit from a height above ground level, such as the batter's shoulder or higher. Since this equation does not include an initial height value, it fails to represent the actual starting point of the ball's trajectory.
3. Simplified factors: The equation assumes a simplified relationship between the height and the horizontal distance. In reality, several factors come into play when hitting a baseball, such as the angle of the swing, the speed of the ball, and the air resistance. Neglecting these factors can result in an inaccurate model that does not accurately depict the complexities of hitting a baseball.
Overall, while the equation may have some mathematical characteristics that resemble a baseball's trajectory, its neglect of vital factors, such as initial height and the complexity of real-world conditions, makes it a poor model for hitting a baseball.