How does wind affect the drag force in a projectile motion problem?

AI Thread Summary
Wind affects the drag force in projectile motion by altering the relative velocity between the projectile and the surrounding air. The drag force is proportional to the square of this relative speed, necessitating adjustments to the equations governing motion. To account for wind, the projectile's velocity must be expressed in relation to the wind's velocity, leading to new expressions for drag force and motion equations. The drag force direction will always oppose the projectile's motion relative to the air. Understanding these dynamics is crucial for accurately solving projectile motion problems in windy conditions.
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1. Homework Statement

Here's the problem: http://www.flickr.com/photos/38401311@N05/5476715833/


2. Homework Equations

Here are the given equations:
http://www.flickr.com/photos/38401311@N05/5477319510/ and
http://www.flickr.com/photos/38401311@N05/5477320730/

3. The Attempt at a Solution

I really don't know where to start on this problem. I thought that maybe you'd just have to subtract the wind velocity vector from the projectile motion velocity vector and add that to the total drag force. Please help!
 
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I'm not having much luck pulling up that flickr page. Can you just write the problem?
 
Ok here's the problem:

Now assume that the wind (air) is blowing with velocity va/0 = αi + βj relative to the ground, where α and β are constants. You may find it useful to consider this problem in terms of the velocity of the wind (air) relative to the ground, va/0, the velocity of the projectile relative to the ground, vp/0, the velocity of the projectile relative to the air, vp/a, and so on.

a) Determine the new drag force, FD, on the projectile assuming that the magnitude of the drag force is now proportional to the square of the relative speed of the projectile to the surrounding air, |vp/a|2. Also, assume that the direction of the drag force is opposite the direction of the projectile relative to the surrounding air.

b) Rewrite (1) and (2) to account for the blowing wind va/0.


Equations:

(1) xdot = vcos(θ) and ydot = vsin(θ)

(2) vdot = -(CDv^2/m) - gsin(θ) and θdot = -(g/v)cos(θ)
 
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