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.
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?