I'm trying to come up with an equation to determine where a ball would land (basically the distance it moves) from a spring loaded projectile launcher set up on a table. I'm looking for "d", and I know the spring constant, compression, mass of the ball, height the ball starts at, angle the launcher is set at, and whatever else I can measure using a meter stick, balance, and protractor. There aren't any numbers just known variables
Conservation of Energy eqn (at least the version I learned in class): Efinal-Eintial=Einput-Eoutput
The Attempt at a Solution
I attempted to use conservation of energy but I get stuck trying to figure out where d goes into be able to solve for it. Also, other online resources use a conservation of energy eqn that has different terms than what I was taught, but I'm assuming they are all the same.
System: Ball and Earth
Initial time: just after ball leaves launcher
final time: just before ball hit ground
And then I'm stuck trying to figure out how the distance goes into this. I'm wondering whether I need to integrate the velocity with respect to time and relate that to the distance since the distance the ball travels is the velocity*time. Any help is appreciated!