Calculating parabolic equations for a trajectory project.

[Andrew Neal]

Homework Statement

I'm a homeschool senior and I'm not starting physics until the second half of the year, so I haven't learned how to do this yet. I'm part of the local Science Olympiad team and I'm heading up the Trajectory project. We have to land the projectile in a certain spot, at a certain distance. The variables will be unknown and will not be given to us until we arrive at the event. Then we have to calculate and calibrate our device ON SITE to launch it at that target.

So this obviously involves parabolic equations, which I'm completely new to. So I'm going to need all the help I can get. I just want to know what EXACTLY to study and wrap my head around. I've been surfing around on Google for about an hour or so but haven't really made much progress due to there being so many different approaches to it.

So what do I need? Well I think I just need a formula where I can plug in all the variables @ the event when I get there. Although I'm not exactly sure that's what I need. So I'm posting here to get a good virtual "slap in the face" and to be pointed in the right direction.

Homework Equations

How to calculate trajectory.

The Attempt at a Solution

Google was my first attempt. Just didn't get very far due to there not being any definitive approach at calculating trajectory.

 

[LowlyPion]

Homework Statement

I'm a homeschool senior and I'm not starting physics until the second half of the year, so I haven't learned how to do this yet. I'm part of the local Science Olympiad team and I'm heading up the Trajectory project. We have to land the projectile in a certain spot, at a certain distance. The variables will be unknown and will not be given to us until we arrive at the event. Then we have to calculate and calibrate our device ON SITE to launch it at that target.

So this obviously involves parabolic equations, which I'm completely new to. So I'm going to need all the help I can get. I just want to know what EXACTLY to study and wrap my head around. I've been surfing around on Google for about an hour or so but haven't really made much progress due to there being so many different approaches to it.

So what do I need? Well I think I just need a formula where I can plug in all the variables @ the event when I get there. Although I'm not exactly sure that's what I need. So I'm posting here to get a good virtual "slap in the face" and to be pointed in the right direction.

Homework Equations

How to calculate trajectory.

The Attempt at a Solution

Google was my first attempt. Just didn't get very far due to there not being any definitive approach at calculating trajectory.

Welcome to PF.

These links might be useful to you
http://hyperphysics.phy-astr.gsu.edu/Hbase/traj.html
http://hyperphysics.phy-astr.gsu.edu/Hbase/trajs.html#tra15

Nothing will be as good however as understanding basic kinematics and vectors first. But if the material there is not too confusing for you, you may be able to dig out what you need.

Good luck.

 

[baba89]

I can understand your frustration with trying to find a definitive approach to calculating trajectory. It can be overwhelming to see so many different methods and formulas out there. However, the good news is that there are some key principles and equations that can help guide you in your project.

First, it's important to understand that a parabolic trajectory is a type of motion that follows the path of a parabola. This type of motion is commonly seen in projectiles, such as a ball being thrown or a rocket being launched. The key to calculating a parabolic trajectory is understanding the forces acting on the projectile and using equations that describe this motion.

One of the most important equations to know is the projectile motion equation, which is used to calculate the horizontal and vertical components of motion separately. This equation is:

x = v*t*cos(theta)

y = v*t*sin(theta) - (1/2)*g*t^2

Where x and y are the horizontal and vertical positions, v is the initial velocity, t is the time, theta is the launch angle, and g is the acceleration due to gravity (9.8 m/s^2).

Another key equation is the range equation, which is used to calculate the horizontal distance traveled by the projectile. It is:

R = (v^2*sin(2*theta))/g

Where R is the range, v is the initial velocity, and theta is the launch angle.

It's also important to understand the concept of initial velocity and how it affects the trajectory of a projectile. The initial velocity is the speed and direction at which the projectile is launched. This can be changed by adjusting the angle at which the projectile is launched or by using a device to increase or decrease the initial velocity.

In your project, it will be helpful to have a device that can measure the initial velocity and launch angle of your projectile. This will allow you to plug in these values into the equations above to calculate the trajectory.

Lastly, it's important to note that in real-world scenarios, there are other factors that can affect the trajectory of a projectile, such as air resistance and wind. These factors may not be accounted for in the equations above, but they can be taken into consideration by making adjustments to the initial velocity and launch angle.

I hope this helps guide you in your project. As with any scientific endeavor, it's important to keep researching and experimenting to find the best approach for your specific project. Good luck!