So if the distance and height are reachable, why are these equations poor models of hitting a baseball:

y = -0.5x^2 + 216x + 3

y = -0.002x^2 + 0.879x + 3.981

y = -0.002x^2 + 0.8732x - 3.981

These equations may not be the best models for hitting a baseball because they make certain assumptions or simplifications that do not accurately represent the real world.

1. The first equation (y = -0.5x^2 + 216x + 3) assumes a constant acceleration due to gravity (-0.5) throughout the entire trajectory of the ball. However, in reality, the acceleration of a falling object like a baseball gradually decreases due to air resistance. This means that the ball's path would not follow a perfect parabolic curve.

2. The second equation (y = -0.002x^2 + 0.879x + 3.981) includes a term to account for air resistance (-0.002x^2), which is an improvement compared to the first equation. However, it still assumes that the air resistance is constant and does not take into account other factors such as wind, temperature, or spin on the ball, which can significantly influence its trajectory.

3. The third equation (y = -0.002x^2 + 0.8732x - 3.981) is similar to the second equation but has a negative coefficient for the last term (-3.981). This negative constant does not have a physical meaning and seems to have been introduced arbitrarily without a proper justification.

To create a more accurate model of hitting a baseball, it would be necessary to consider more parameters such as air resistance, spin, launch angle, initial velocity, and other factors that affect the flight of the ball. Advanced modeling techniques, such as computer simulations or experimental data analysis, can be used to better understand and predict the behavior of a baseball in flight.