1. ## Catapult Formula

Hey there!
I'm kinda stuck on a problem that I've tried to overcome. I built a catapult (and I'm very proud of myself) that only uses a counter weight on it's main arm, which is 20 inches long. I want to make up a mathematical equation to go with my catapult, in respect to the counter weight and the object being thrown. Please help!

Details: Counter weight (bag of marbles): 2KG
Arm length: 20 inches
Distance it can throw: 4 meters +
Object thrown: 50grams +

So the formula I had in mind would be in algebra, right? So I could replace the letter with the corresponding numeral. Example: w (weight) = 2KG.

Any help would be appreciated!

2. Originally Posted by RAz
Hey there!
I'm kinda stuck on a problem that I've tried to overcome. I built a catapult (and I'm very proud of myself) that only uses a counter weight on it's main arm, which is 20 inches long. I want to make up a mathematical equation to go with my catapult, in respect to the counter weight and the object being thrown. Please help!

Details: Counter weight (bag of marbles): 2KG
Arm length: 20 inches
Distance it can throw: 4 meters +
Object thrown: 50grams +

So the formula I had in mind would be in algebra, right? So I could replace the letter with the corresponding numeral. Example: w (weight) = 2KG.

Any help would be appreciated!
I've attached a sketch of the catapult as I imagine it could look like

Do you know already the length of x?

Or do you want to know the length of x so the "muzzle" speed is a maximum? Then the counterweight of $2 \cdot 9.81\ N$ and the weight of the "bullit" must be considered as constant. Right?