Projectile motion: find distance a ball would land

[phys1213]

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: 1/2mv²
Spring: 1/2kx²

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_f²
E_initial= 1/2mv_o²+1/2kx²+mgH
E_input-E_output=0
1/2mv_f²-1/2mv_o²-1/2kx²-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!

 

[BvU]

Hi phys,

Not bad for a first post. Yes, you need some projectile motion equation to complete this. From initial E_initial= 1/2mv_o²+1/2kx²+mgH (where v_o = 0 ?) you get v₀. And your projectile trajectory is uniform motion horizontally (needing t) and uniformly accelerated vertically (which gives you a quadratic equation for t) .