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

 

[PJC01]

As a scientist, there are several variables that you need to consider for your projectile motion project. These include the initial velocity of the projectile, the angle of launch, the mass of the projectile, and the air resistance. Additionally, you will need to take into account the properties of the siege weapon you are using, such as the length of the arm and the force applied by the tension in the ropes or springs.

To calculate the tension needed to launch the water balloon, you will need to use the principles of Newton's laws of motion. The tension in the ropes or springs will act as the force that accelerates the projectile, and the amount of tension needed will depend on the mass of the projectile and the angle of launch. You can use equations such as F=ma and the kinematic equations to determine the necessary tension for your desired distance.

It is also important to consider the accuracy and precision of your measurements and calculations. You may need to repeat your experiments multiple times to get reliable data and ensure that your results are reproducible. Additionally, you should take into account any sources of error, such as variations in the tension or the angle of launch, and try to minimize them to improve the accuracy of your results.

In conclusion, to successfully complete your projectile motion project, you will need to carefully consider all of these variables and use scientific principles and equations to accurately calculate the tension needed to launch the water balloon to your desired distance. Good luck with your project!