Spring launcher equation for x so it hits the target

[firezap]

Homework Statement

I need to find out how far to pull the spring back so it will travel to the target. The launcher and the target is both set on the floor. The spring is the projectile. I will be given the distance on the day of testing. i should take into account air resistance so i will be more accurate.

Mass of spring = 0.024kg
k = 25N/m
launch angle set at 40 degrees
length of spring when not stretched is 0.20m
height of launcher is 0.54m
My trials pulling spring back and recording distance
.25m went .52m
.3m went 1.67m
.34m went 2.2m
.4m went 4.78m
.43m went 5.37m

Homework Equations

conservation of energy
Es = Ek
1/2mv^2 = 1/2kx^2
projectile motion
d = v1xt
v1x = v1cosӨ

The Attempt at a Solution

1/2mv^2 = 1/2kx^2
i get stuck on this part. plugging in numbers but i do not have the velocity. What i do next?

 

[haruspex]

Is the target at floor level?
You need an equation relating to vertical motion, relating initial speed, acceleration, time and height difference.

 

[firezap]

yes it's on the floor