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A projectile with an unknown mass is launched 90 degrees vertically to a height of 0.650 m with a spring deformation of x = 0.031 m. The initial speed of the projectile is v_{0}=3.6 m/sec and the projectile is resting on top of the spring gun "holder" before launch. Find the spring constant k.

2. Relevant equations

W = d*F, P = F*v*cos(θ), W = E_{pot}, a_{y}=-g, P=ΔE/Δt, E_{total}=E_{kin}+E_{pot}.

3. The attempt at a solution

I don't know exactly how to handle this problem, but I've been trying to attack it from many many angles with W = d*F, P = F*v*cos(θ), W = E_{pot}, a_{y}=-g and the relationship between distance, velocity, acceleration and time but it all comes down to me missing the mass and the force in every equation with at least two unknowns in every case. The closest I ever got was to realize that W being done on the projectile = E_{pot}that the spring has before launch and wondering if I could use the W=d*F to figure out the F-value so I could figure the rest of the equations out but

P=F*v seemed plausible as well hoping that cos(θ) = 1 in case of the angle being 0 but I gave up on that because it said in my formulae book that I need a particle with a speed in order to use it and the projectile is a static particle after all.

So what do I do?! It's very important that I hand this in as I might not be able to continue my class if I don't and I prefer doing it on my own but I've come to a point spending hours and hours where I simply don't know what to do ... Maybe I'm just stupid and can't see the solution right in front of me but it really seems hard to me ... Please help! It's really urgent!

Oh and I also got a clue from the teacher: Consider energy relations when you solve this problem. And I did and I still have no answer.

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# Find spring constant, unknown projectile mass, vertical spring gun.

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