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## Homework Statement

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

## Homework Equations

Conservation of Energy eqn (at least the version I learned in class): E

_{final}-E

_{intial}=E

_{input}-E

_{output}

F=ma

F

_{g}=mg

sinθ=v

_{oy}/v

_{o}

cosθ=v

_{ox}/v

_{o}

KE: 1/2mv

^{2}

Spring: 1/2kx

^{2}

## 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

E

_{final}=1/2mv

_{f}

^{2}

E

_{initial}= 1/2mv

_{o}

^{2}+1/2kx

^{2}+mgH

E

_{input}-E

_{output}=0

1/2mv

_{f}

^{2}-1/2mv

_{o}

^{2}-1/2kx

^{2}-mgH=0

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!