How Much Counter Weight is Needed for a Trebuchet to Hit a Specific Distance?

[Water Man]

Homework Statement

We need to find the mass of the counter weight needed to make our projectile go a certain distance.

Height = 22.5cm (The height of arm off the ground)
Distance needed to travel = 1m/100cm and and 50cm
Angle above horizontal = 32 degrees
Projectile mass (small ball) = 125 grams
Counter Weight mass = WHAT WE ARE CHANGING


We don't know velocity or anything else like that. How can we find out how much mass to put on the counter weight to make it travel a certain distance? Also please give equations/units. This is really bugging me. I tried many things and formulas but nothing seems to be working for me.


What I've tried

I tried using a lot of formulas but so far all my stuff is theoretical. I know I can find velocity using distance/time but I can't do it like that because I still haven't gotten it to launch that far. I have stumbled upon lots of formulas and tried some from this PDF:

[PLAIN]http://www.algobeautytreb.com/trebmath35.pdf

[/PLAIN]

But a lot of the stuff is too advanced and isn't specifying units. The one formula I did try was this: Range = 2 * (Counter weight mass/projectile mass) * h.

Height = the height the counter weight falls to.


However, the result's I'm getting seem very off.

 

[RTW69]

The article you cite is a useful resource.

I assume the 32 degree angle is the angle the projectile leaves the Trebuchet, call it "A". For projectile motion the Range,R = (2*Vo^2*sin(A)*Cos(A))/g

Solve for Vo

The KE of the projectile= M2*Vo^2/2 where M2 is the projectile mass

The PE of the counter weight is M1*g*h where M1 is the counter weight mass

Theoretically all the PE of the counter weight goes to the KE of the projectile. Setting them equal gives.

M1=(M2*Vo^2)/(2*g*h)

The article also describes a method of calabrating the Trebuchet by determining a range efficiency, eff. You need to fire the Trebuchet and measure the range for a given M1.

A new M1=(M2*R)/(2*h*eff)