Impact of several variables on resulting projectile motion trajectory

In summary, the variables air resistance and wind speed have an impact on the final position of the projectile, but the effect of these variables is different depending on the height of the projectile.
  • #1
Badgun
2
0
Homework Statement
I have a program to model a Projectile Motion with air resistance (numerically calculated) and also with wind influence (adding wind speed to the current speed if the projectile is above some height). I have a homework to analyze the influence of several variables on the resulting trajectory (basically the final x value when it impacts the ground). I mean variables like the weight, the drag coefficient, elevation angle or the wind.
Relevant Equations
I think there aren't any equations needed for this problem.
I was told to generate these variables (m, C, alpha, wind velocity) normally distributed and compare the random data with the result and then tell, which of the variables has the most impact. Here I am stuck, tried to compare variances, kurtosis and skewness of the data (the original variables and the final x), but I don't really know, what the numbers or the differences between them really mean. I'm not really good at statistics, like I don't understand the principles of statistics. Can you suggest me a method of comparing those influences to be able to tell which of the variables has the most influence? Thank you really much!
 
Physics news on Phys.org
  • #2
The simplest things to understand and discuss would be the mean and the standard deviation (square root of the variance).

The mean is the average. So you are just looking at how far, on average, that effect causes the landing spot to move. Now they're on different scales but you can still say something qualitative like "a 1% change in this variable causes only a 0.5% change in the position, on average, but a 1% change in this other variable causes a 10% change".

Standard deviation measures the spread of the distribution for a given fixed value of one of the variables. Again you could try to come up with some way to compare them, like a percentage, to compare how the spread of one random variable affects the spread of the final position.
 
  • #3
RPinPA said:
The simplest things to understand and discuss would be the mean and the standard deviation (square root of the variance).

The mean is the average. So you are just looking at how far, on average, that effect causes the landing spot to move. Now they're on different scales but you can still say something qualitative like "a 1% change in this variable causes only a 0.5% change in the position, on average, but a 1% change in this other variable causes a 10% change".

Standard deviation measures the spread of the distribution for a given fixed value of one of the variables. Again you could try to come up with some way to compare them, like a percentage, to compare how the spread of one random variable affects the spread of the final position.

Thank you, I didn't realize I can do that this way, I hope this will satisfy what my lector wants :)
 
  • #4
Badgun said:
with air resistance (numerically calculated) and also with wind influence (adding wind speed to the current speed if the projectile is above some height).
I know you were not asking about the equations for this, but a trap some fall into is treating the horizontal and vertical motions as independent when there is drag. They can be independent, but it depends on the drag equation used (linear or quadratic).
 

1. How do different angles affect the trajectory of a projectile?

The angle at which a projectile is launched greatly affects its trajectory. A higher angle will result in a longer flight time and a higher apex, while a lower angle will result in a shorter flight time and a lower apex. The optimal angle for maximum distance will depend on the initial velocity and the force of gravity.

2. What is the effect of air resistance on the trajectory of a projectile?

Air resistance can have a significant impact on the trajectory of a projectile. As the projectile moves through the air, it experiences a force in the opposite direction of its motion, slowing it down and altering its trajectory. The effect of air resistance increases with the speed and surface area of the projectile.

3. How does the initial velocity affect the trajectory of a projectile?

The initial velocity, or speed, of a projectile has a direct impact on its trajectory. A higher initial velocity will result in a longer flight time and a greater distance traveled, while a lower initial velocity will result in a shorter flight time and a shorter distance traveled. The angle of launch and the force of gravity also play a role in determining the trajectory.

4. What is the relationship between mass and trajectory in projectile motion?

The mass of a projectile does not directly affect its trajectory. However, a heavier projectile will require more force to be launched at the same initial velocity as a lighter projectile. This means that the initial angle and velocity may need to be adjusted to achieve the desired trajectory for a heavier projectile.

5. How does the force of gravity impact the trajectory of a projectile?

The force of gravity is a crucial factor in determining the trajectory of a projectile. It constantly acts in a downward direction, causing the projectile to follow a curved path. The strength of gravity can also be affected by the mass and distance between objects, which can alter the trajectory of a projectile accordingly.

Similar threads

I Statistical modeling and relationship between random variables
    • Set Theory, Logic, Probability, Statistics
Replies
7
Views
458
Finding two variables in projectile motion
    • Introductory Physics Homework Help
Replies
23
Views
3K
What is the formula for determining the force of impact in a physics problem?
    • Introductory Physics Homework Help
Replies
9
Views
939
Projectile motion collisions problem
    • Introductory Physics Homework Help
Replies
19
Views
2K
Projectile Motion: Salmon Jumping a Waterfall - Calculating Minimum Speed Needed
    • Introductory Physics Homework Help
Replies
2
Views
1K
Projectile motion with air resistance
    • Introductory Physics Homework Help
Replies
12
Views
2K
I Desirable estimator properties...
    • Set Theory, Logic, Probability, Statistics
Replies
7
Views
480
Projectile Trajectory (I'm confused about the lab report)
    • Introductory Physics Homework Help
Replies
5
Views
6K
Report on air resistance of projectile motion
    • Introductory Physics Homework Help
Replies
2
Views
2K
Projectile with air resistance
    • Introductory Physics Homework Help
Replies
22
Views
4K

Hot Threads

Recent Insights

Back
Top