and the ball doesnt go more than about 60 km up (so that gravity is constant), then the function will always be height = Ax^2 + Bx + C.The numbers for A, B, and C depend on the situation.Usually A is -16.......
Other formulas such at the one you mentioned are determined by understanding the physics of motion. Gravity can be measured and then the position is a function of the initial velocity and position.
Each of them comes from a lot of observations and trial and error. When equations are finally found and agreed upon the inventors are recognized by having the equations named after them, such as Einstein's Relativity equation or Kepler's equations of planetary motion.
If you ignore air friction, and the ball doesn't go more than about 60 km up (so that gravity is constant), then the function will always be height = Ax^2 + Bx + C. The numbers for A, B, and C depend on the situation. Usually "A" is -16.087 ft/sec^2, which rounds to -16, and "B" and "C" depend on the initial speed and position.
The people who write the problems don't actually go out and perform the experiment and measure the results. That was all done hundreds of years ago, by people like Galileo and Newton.
This particular equation is the result of a physics process where information already exists about the magnitude of acceleration due to gravity.
But you could collect some data. For a parabola, it only takes three points, and you can derive the parabolic equation.
math is so had subject.
