High school physics problem involving a spring slingshot

[Kailford]

Homework Statement

For a grade 12 physics project we have to stretch a spring along an inclined plane and then let go so that it hits a target. I know the mass of the spring, the angle of the incline, the height of the incline (how high the front of the spring would be off the ground before launching) the spring constant, and the distance from the target. Using this information, I need to figure out how much to stretch the spring to hit the target. How do I do this?

Homework Equations

Es = (1/2)kx^2
Eg = mgh
Ek = 1/2mv^2
Fs = kx
Fnet = ma
d = 1/2(v1 + v2)t
v2 = v1 + at
d = v1t + (1/2)at^2
d = v2t - (1/2)at^2
v2^2 = v1^2 + 2ad

The Attempt at a Solution

I have tried splitting the spring force into x and y components and then using that to find the acceleration, but that simple results in 2 variables (the acceleration and the amount the spring needs to be stretched). I have also tried using the different kinematic equations to try and find the velocity so that I can use it to find x by setting (1/2)kx^2 equal to (1/2)mv^2, but all of those equations either have v, t, or both as variables, and I am unable to solve for those.

 

[Brian T]

The steps you're doing seem okay, you just need more info. You could try figuring out the initial velocity by seeing how much work the spring does up until the point of release (and then applying the work KE thm)

 

[Kailford]

The steps you're doing seem okay, you just need more info. You could try figuring out the initial velocity by seeing how much work the spring does up until the point of release (and then applying the work KE thm)

Thanks Brian! I am at a loss as to how I would do that, though. As far as I know I need to know how much the spring is stretched to determine the work of the spring before release, but the stretch of the spring is one of my variables.

 

[haruspex]

Thanks Brian! I am at a loss as to how I would do that, though. As far as I know I need to know how much the spring is stretched to determine the work of the spring before release, but the stretch of the spring is one of my variables.

You can follow that line, expressing the speed as a function of the unknown variable x (the initial spring extension). From there, obtain the distance as a function of x, and see what x gives the desired distance.

I have also tried using the different kinematic equations to try and find the velocity

That's the way I'd do it, working backwards. Remember you can write kinematic (SUVAT) equations for vertical and horizontal. They share the time variable, so you can eliminate that between them. That should give you enough information.
The trick with SUVAT equations is to pick the one that involves the four variables of interest. Since you need to set the times equal, you'll want t involved in each. Post some attempt.