How to find muzzle velocity of homemade launcher

[appleallie]

So, I made a marshmallow launcher that has a small tube within a larger tube that when a bungee is released it gets launched into the larger tube, smacking the marshmallow and sending it flying. Woo!

My problem is that I want to use the equations for projectile motion, I know the angles I'm firing at and my force is consistent. The only problem is that I don't know the force on the marshmallow or the muzzle velocity! :(

I have the spring constant and don't need to solve the numbers right now, just need help setting up equations.

Here's a picture!

http://tinypic.com/r/245aotl/7

http://tinypic.com/r/245aotl/7

and some dimensions!

http://tinypic.com/r/wlrszb/7

 

[Delphi51]

Looks great! Welcome to PF.

If you want to predict the speed from the design, you would probably work with energy. How much work is done pulling the cord back, how much is lost to friction when shooting, leaving how much kinetic energy with the piston. From that you could calculate the speed of the piston and marshmallow.

It might be easier and more accurate to work back from the trajectory. Could you shoot a rock or something that has much less significant air resistance? Using the maximum horizontal distance and the shooting angle, you could calculate the initial speed.

 

[appleallie]

oh yeah... i could use the equation for range correct?

r=[(v^2)/g]*sin(2$\theta$)?

or would I use displacement in the x-direction?

Δx = v$_{ox}$t