Physics, how to link the tension from an elastic band to the velocity of a projectile launched from it

I have built my own catapult from wood and to create tension, i need to link the catapult arm to the base using an elastic band and pull the arm down to place it under tension, and by releasing the arm the projectile (a marble ball) is launched at a certain velocity. My problem is that i need to find the initial velocity of the projectile. How could i calculate the tension created by the elastic band and find the initial velocity of the projectile using such?

would i have to use hooke's law F=-kx
or would i use Potential Energy PE=1/2mv^2

i thought that through hooke's law i could find the tension of the elastic band (F) and through PE i could find the velocity (v) but kind of stuck and confused...

Please help, this is important for my lab report. thanks

The elastic energy will equal the kinetic energy of the projectile:

½k*x² = ½m*v²

v = x*√[k/m]

Note: The above assumes there is no energy loss due to friction. impact, etc..........

Steve, the m in your equation relates to the mass hung from the elastic band, my issue is that i am pulling the elastic band back with my force and can't figure out how to calculate m....

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