Calculating Velocity, Range & Height of a 2kg Projectile & Counterweight

[>>>SiM>>>]

Homework Statement

Example:

2 kg projectile
2 kg Counterweight
Dropped from 1m
45 Degree Angle
9.8 m/s Gravitational Acceleration

(For a catapult)

Homework Equations

My science teacher's equation was blatantly wrong in a number of ways, so I no longer have it.

The Attempt at a Solution

When I use his formula, not only does the velocity come out wrong, but the range is completely inaccurate, especially when the Gravitational Acceleration is altered. For example, changing the Gravitational Acceleration up or down seems to make the projectile go faster and farther, which makes no sense to me, since making it bigger should make it's distance less. Changing the Gravitational Acceleration to a negative number gives a negative answer which is wrong as well.

What I need to know is a working formula that will calculate the velocity, range, and maximum height of a projectile fired with the given five values (Mass of Projectile, Mass of Counterweight, Height the counterweight is dropped, Gravitational Acceleration, and Angle of launch). I attempted to find an answer on the internet, but then got confused trying to piece together the different formulas to fit my needs. If I have the formula, I intend to figure out the answers to all the questions myself.

He isn't available for contact so I can't ask him for a working formula myself, and I can imagine how frustrated my classmates are. My friend asked me to tell him as soon as I get an answer.

 

[lzkelley]

Please be more precise on your problem specification, its quite ambiguous.

 

[>>>SiM>>>]

Please be more precise on your problem specification, its quite ambiguous.

I need a formula which will calculate the initial velocity of the projectile (m/s), the range of the projectile (meters) and the maximum height the projectile will reach (meters) using the Mass of the Projectile and Counterweight (kg), the height from which the counterweight is dropped (meters), the Angle it was fired (degrees), and the Gravitational Acceleration (m/s).

 

[lzkelley]

The only way to solve the situation with the given information is to use conservation of energy (which won't give a very accurate result).
Assume that the potential energy of the counterweight is completely converted to kinetic energy of the projectile. Groovy?