What is the equation for a spring launcher?

[Riman643]

Homework Statement

What is the generalized equation of the initial launch speed for a spring launcher at different angles? Use PE of the spring, mass, and angle in the equation.

Relevant Equations

Ei = Ef
PEspring = 1/2 kx^2
KE = 1/2 mv^2

I am really stuck and confused. I just need the equation. Thanks!

Here is my attempt at solving:

PEspring = 1/2m(Vx^2 +Vy^2)

 

[Chestermiller]

Problem Statement: What is the generalized equation of the initial launch speed for a spring launcher at different angles? Use PE of the spring, mass, and angle in the equation.
Relevant Equations: Ei = Ef
PEspring = 1/2 kx^2
KE = 1/2 mv^2

I am really stuck and confused. I just need the equation. Thanks!

What have is your assessment so far?

 

[Riman643]

This is my attempt

PEspring = 1/2m(Vx^2 +Vy^2). I know this is not right. I am confused and have been trying to figure this out for two days now. I do not know how to incorporate the angle of the launcher.

 

[Riman643]

So here is my next attempt

PEspring = Wgrav + KE
(1/2)kx^2 = mgsin(theta)x + (1/2)mv^2

Is this correct?

 

[haruspex]

So here is my next attempt

PEspring = Wgrav + KE
(1/2)kx^2 = mgsin(theta)x + (1/2)mv^2

Is this correct?

Looks right.