Trying to find the amount of stretch of a spring for a launch

[Ace.]

Homework Statement

I'm doing an experiment where I have to calculate the stretch of a spring needed for it to launch itself into a trashcan located some distance away. The spring is located on the edge of a ramp that is 1.13 m high. The angle of the ramp is 30 degrees above horizontal. The spring constant of the spring is 175 N/m. The trashcan is located a horizontal distance 5.85 m away, height of the trashcan can be ignored. I must find the stretch (x) of the spring that will allow it to launch itself and land in the trashcan.

Homework Equations

Ee = (1/2)kx^2
Ek = (1/2)mv^2
Eg = mgh
Fx = kx (spring equation)

The Attempt at a Solution

At first I thought I must solve for time of flight but there are too many variables involved. For instance, I don't know the initial velocity of the spring. If I could solve for time, then I could use it to find Vx (horizontal component of velocity), and then use the angle to find V. Then I would do Ee = Ek (elastic potential was converted to kinetic the instant the spring was released) and finally solve for the stretch (x).

I tried to use the range equation: R = (v^2/g)sin2θ in hopes of finding V, but that is only for projectiles that land at the same height. Any guidance on how to approach this?

 

[jackarms]

Think of the problem in two steps. First, see if you can find the magnitude of the velocity as the spring leaves the ramp. You know the velocity will be directed 30 degrees above the horizontal, and where the spring will land, so see if you can solve for v. You can eliminate the time variable with two equations.

Then think about how much work the spring has to do to give itself that initial velocity. If it has to move up the ramp first before leaving, you'll also have to involve the increase in potential energy.

 

[PhanthomJay]

After finding the required initial speed in the first step per jackarms hints, you then need to use conservation of energy to determine the spring stretch required. But since the object being launched is the spring itself, you need to know the mass of the spring, and the solution is perhaps beyond the intro physics level type spring problems which typically deal with massless springs.