# Deviation from 2D trajectory [closed]

I need to find out how far a ball is from the predicted trajectory in 2 dimensional space and I know the start and end position of the ball in both dimensions. Along with that I know the initial velocity and the angle at which the ball was launched.

Every single variable is known in this picture.

The problem is that I can predict where the ball is going to land based on the angle α and the initial velocity v0, but the actual landing is a bit off due to variables assumed to be zero (wind, friction, etc.) and I need a mathematical way of calculating this deviation.

NOTE: The mathematical model may not include calculus as we haven't covered that part of our curriculum yet.

Any suggestions on how to do that?

• This may be off-topic, but... what exactly are $x_\text{slut}$ and $y_\text{slut}$?!
– Danu
Commented Aug 29, 2014 at 21:21
• More to the point: What's wrong with just calculating by how much percent your predictions are off, given the actual data? Another often-used, basic method from error analysis is using the standard deviation.
– Danu
Commented Aug 29, 2014 at 21:22
• Are you trying to make a mathematical model to figure out by how much your original mathematical model is off by? Commented Aug 29, 2014 at 21:23
• @Danu slut is Danish for end Commented Aug 29, 2014 at 21:25
• Okay. The key words here are (once again) error analysis. There's a famous, basic textbook by Taylor on this subject
– Danu
Commented Aug 29, 2014 at 21:26

It is worth noting that the force due to air resistance is usually modeled as $$\vec{F} \propto -\vec{v} \ \ \ \text{or} \ \ \ \vec{F} \propto -|v|^2 \hat{v}$$ Intuitively this makes sense: the faster you go, the more drag you should experience. The minus sign means that the force acts in opposition to the direction you are travelling.