What variables do I need to consider for my projectile motion project?

[marcusnguyen]

I'm new to this place so I really didn't know where to post this but here's the deal. My Physics teacher assigned us a projectile related to projectile motion. We are to build a siege weapon (catapult, trebuchet, ballista, etc.) that would launch a 1lb water balloon 25 ft in distance. We are planning to build a ballista and we know that to get the furthest distance, the ballista must be angled at 45 degree. However, I am having trouble understanding how the tension stuff works to calculate how much is needed to send the water balloon flying far enough to get a 100 on the project. Can someone please help me?

 

[rock.freak667]

From the formula for the range, you can get the speed required. Conservation of energy can then be applied to find out how far you need to stretch the object back before it can get enough energy for the correct speed (assuming a sling-shot type thing is used).

If I remember correctly the formulas are

$$R = \frac{v_0 ^2 sin 2 \theta}{2g}$$

$$\frac{1}{2}{m}{v^2} = \frac{1}{2} kx^2$$

$$T = kx$$

 

[marcusnguyen]

Can you please tell me what those variable mean?

 

[rock.freak667]

Can you please tell me what those variable mean?

R= range
v₀, v = initial velocity
θ = angle of launch
g = acceleration due to gravity

k = spring constant of material
x = extension
m = mass

T = tension