Angle, range and extension in projectile motion?

[donkeycopter]

We have a trebuchet which we can adjust the launch angle, and how far the rubber band is pulled back (extension). The rubber band spring constant is constant throughout. I need to find the relationship between the angle of launch and range, and the relationship between the extension and range. This should allow me to finally be given a range, and adjust the angle and extension so as to make the mass land at that spot.
We are given no equations, but I have been using the kinetic and gravitational potential energy equations.I have trial data in which I have calculated the spring constant - at 184 n/m.

I have calculated an equation which shows EPE = Fx/2 (the area under the trial data graph is EPE, as it is a force (F) vs extension (x) graph).

On the net I found the equation: u = \sqrt{Rg/2sin20}

R-range
g-gravityHow should I go about solving this? We need to collect data from repeated tests etc, its an investigation.

Thanks a lot! :)

 

[rock.freak667]

The energy in the spring is 1/2kx² which is converted into KE as the mass leaves the rubber band.

so you will have by conservation of energy 1/2kx² = 1/2 mv² with v being your initial velocity.

 

[donkeycopter]

The energy in the spring is 1/2kx² which is converted into KE as the mass leaves the rubber band.

so you will have by conservation of energy 1/2kx² = 1/2 mv² with v being your initial velocity.

So I shouldn't get the speed at the top of the ramp, so it would be KE + MGH?

What else can I do?