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I need to get the x/y values of a fired projectile given the angle of the initial power, and air resistance.

The formulas I have are

$$V_x=V_o \cos\theta$$

$$X=V_o \cos \theta t$$

$$V_y=V_o \sin \theta -gt$$

$$Y=V_o \sin \theta t-(1/2)gt^2$$

To calculate the initial velocity $V_o$, I did

$$V_o= \sqrt{2E/m}$$

where

$E$ = power with which the ball was fired, $m$ = mass of ball

What I need is how to add air resistance to this equation

Besides, are my equations correct?

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Note that Physics.SE uses to MathJax to provide LaTeX-like formatting of mathematical expressions. I've fixed up this post; you should learn to use it if you are going to participate on Physics.SE. –  dmckee Apr 9 '11 at 17:08
    
I think that your equations are not correct. Shouldn't $V_x,V_y$ be derivatives of $X,Y$? They surely aren't in your case. They're related by transformations that resemble the deletion of random characters. ;-) Moreover, $\theta$ seems to be dimensionless from some equations and frequency from other formulae. –  Luboš Motl Apr 9 '11 at 18:20
    
@Luboš, I interpreted Smith's equations as $X = (V_0 \cos\theta) t$ and $Y = (V_0 \sin\theta) t - (1/2)gt^2$ –  Keenan Pepper Apr 9 '11 at 18:56
1  
What is this "Power" in headline or later last equation? It looks like energy! –  Georg Apr 9 '11 at 20:24
    
Try chapter 1 here: books.google.com/… –  Mark Eichenlaub Apr 9 '11 at 23:22
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closed as too localized by David Z Apr 9 '11 at 23:29

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1 Answer

In order to add air resistance (drag), you have to have some specific model of air resistance in mind. Which model you choose depends on how accurate you want to be and which different fluid dynamics phenomena you want to describe.

Often people model the drag in the simplest possible way, as a force proportional to the velocity but in the opposite direction: $\mathbf{F} = -b \mathbf{v}$ This is known as Stokes drag and is only approximately true at low velocities (low Reynolds numbers). At higher velocities the drag force becomes proportional to $v^2$ rather than $v$, and if the velocity ever approaches the speed of sound, the situation becomes more complicated with the possibility of shocks forming.

Your equations all appear correct, but it will probably be difficult to generalize them to include drag, even with as simple a model as Stokes drag. Depending on what you're planning to use this for, it might be much more straightforward to integrate the equation of motion numerically. Look up "numerical ODE solving" or "Euler method" for a specific example.

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actually, am just trying to do a little simulation of how air can affect projectiles, it shouldn't be too much complected. if i can use a constant as the coefficient of the air drag say 0.015, i'd be ok –  Smith Apr 11 '11 at 12:25
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