Not sure if this is the right place to post this, but will give it a shot. I am helping out my little sis this weekend as she has an egg launcher project for high school. There are weight and dimension limitations of course, and I'm not quite clear on other rules (when I took this class ~8 years ago we made an air cannon, but I'm pretty sure those aren't allowed no). So I was thinking a slingshot. I want to figure out the initial velocity after gravity was the only thing acting on it so I could find: x(final)=V(intial)^2*sin(2theta)/g and get an idea what kind of springy material I would need. With acceleration=k (L2-L1)/m I was going around in circle trying figure out a way to get L2 (L2 being the extended length and L1 its rest legth) as a function of time, so I could integrate it. So I was thinking I could say this is a SHO and it has a solution of x(t) = A cos (w0*t) ignoring phase because its staring at its maximum displacement? Then assuming that the prjectile have left the slingshot apparatus when L2=L1 or pi/2 I think, and just take v(intial) at pi/2 (ignoring time really knowing v is going to be at max) as v=A*w0. Giving me an initial veloicty as it exits the slingshot of: v=(L2-L1)*(k/m)^(1/2) Hope this is clear enough, I just wanted someone elses input. Or maybe someone knows a good way to get force(t) of a spring as it is contracting. The max dimensions are rectangular not square so I should probably figure out the difference between a larger k, smaller angle, and a 45 degree angle and a smaller k.