Solve Spring Gun Question Homework

[Oliviam12]

Homework Statement

A spring-loaded toy dart gun fires darts with a mass of 104 g. When the spring in the dart gun is compressed 8 cm, the dart flies off with a speed of 11.4 m/s. What is the spring constant of the spring in the dart gun?

Homework Equations

W=1/2*k*x^2
V=sqrt(2W/m)

The Attempt at a Solution

Not really much of a clue on how to do this problem, I tried to use this example;

A spring with spring constant 218.5 N/m is compressed by 0.291 m. Then a steel ball bearing of mass 0.0733 kg is put on the spring, and the spring is released. What is the speed of the ball bearing right after release? (The ball bearing will come off the spring exactly as the spring returns to its equilibrium position. We will assume that we can neglect the mass of the spring in this calculation.) W = 1/2*k*x^2 then us this equation: v = sqrt(2W/m)

I found on Google and work backwards but, it got confusing and messy. I did find the
kinetic energy to equal 6.7 J, but I don't think I need it?

 

[Astronuc]

If one assumes conservation of energy and no losses due to friction (i.e. dissipative forces), then the energy stored in the spring become kinetic energy of the dart.

Equate the stored energy of the spring and the kinetic energy of the dart.

 

[Oliviam12]

Thanks! That tip kind of caused an epiphany and I got it now.