Finding the Spring Constant of a Water-Balloon Launcher

[Minte]

Homework Statement

Find the average spring constant (k) of a water-balloon launcher, and use that to find the distance to pull back the launcher and launch a balloon of a certain weight a certain distance. I'm at the "finding k" part.

Diagram attached.

Known:
Weight of balloon (Fw, N), mass of balloon (m, kg)
Height of launcher (H, m)
Length of pullback (B, m)
Angle Theta (since tan Th = h/B)
Flight distance / range (x, m)

Unknown:
Spring constant of launcher (k, N/m)

Homework Equations

F=kx
U=kx^2/2
?

The Attempt at a Solution

I just can't find a place to start substituting equations. I tried converting spring energy to gravitational / kinetic energy, but the formulas got very complicated very quickly and lots of extra variables (such as velocity, time, and acceleration) were introduced. I don't think that I can use Fw for Fs, otherwise, why would the pullback distance matter?

I have a lot of data (a whole day on the baseball field hurling water balloons worth), but I don't know how to find the spring constant! Once I have a formula, the rest will be a breeze, but there are too many options, which always makes my brain explode.

Solved
It turns out that the teacher had a formula that he wasn't giving us. k=Fwx/2BH, I think. Anyway, it has been solved. Thanks for the help, anyway! =D

 

[Delphi51]

It seems to me you could begin with spring energy = kinetic energy given to the balloon. That gives you the initial velocity as an expression with a k in it. From the initial v, you can do a standard 2D projectile motion calc to find the horizontal flight distance x in terms of k and the angle. This expression could be solved for k so you could calculate a value for v and then k from each of your test shots (where you know the angle and x).