Air-wind-blah velocity problems

[Pseudo Statistic]

OK, I've been thinking about these specific problems a lot lately..
Hope someone can help clarify how I should understand how to go about these kinds of questions..

Let's say an airplane is moving at some angle x degrees with respect to the east (Stupid way to describe the direction, please don't blame me. :P) and it's moving at a velocity v...
Let's say the wind is blowing, hmm, south...
Because of the wind, wouldn't the plane be moving in another direction, which would mean it would never ever ever reach its destination s meters away at the direction it was supposedly to travel in unless it were to change its route?

This is where I'm wondering how to solve problems like...
Say a person is walking with velocity magnitude 20m/s at 53 degrees and there's a wind vector w = -5i m/s which is applied to this person..
Let's pick an arbitrary distance, err... 300m that he is from his destination..
How would we find the time it takes for him to get to his destination?
I was thinking finding the x and y components to his velocity and adding up the two vectors and finding the resultant and dividing 300m by it, but that resultant velocity would be in a whole new direction!
This is really confusing me... I really want to learn how to approach these problems...
I'd appreciate it if someone could help me out.. (and perhaps provide examples of these kinds of problems)
Thanks.

 

[whozum]

Let's say an airplane is moving at some angle x degrees with respect to the east (Stupid way to describe the direction, please don't blame me. :P) and it's moving at a velocity v...
Let's say the wind is blowing, hmm, south...
Because of the wind, wouldn't the plane be moving in another direction, which would mean it would never ever ever reach its destination s meters away at the direction it was supposedly to travel in unless it were to change its route?

You're right, that's why they fly at a certain angle to compensate for wind. Same thing in golf.

How would we find the time it takes for him to get to his destination?

You know the final velocity vector that you 'want', and the vector that he HAS (his speed), so break it down into components and add to it the effect of the wind. You'll want this vector (the sum of the other two) to equal your final velocity vector. If he is getting pushed to the east then you'll want him to walk in a direction a little to the west of where he is going.

 

[Pseudo Statistic]

So in the case of this arbitrary problem of the person walking... can you tell me how to find this angle?

 

[whozum]

[itex]v_{man} = < 20\cos(53) , 20\sin(53) > [/tex]<br /> [itex]v_{wind} = < -5 , 0 > [/tex]<br /> [itex]v_{net} = < 20\cos(53) - 5, 20\sin(53) > = < 7.04 , 16 > [/tex]<br /> <br /> If he walks along his vector, he'll end up traveling along that net vector. He started off walking at 53 deg relative to the axis, but ended up walking along a line 63 deg relative to the x axis, which makes sense since the wind is pushing him left.<br /> <br /> To find how long it takes him to walk 300m along that line, just divide the distance by the velocity.[/itex][/itex][/itex]

 

[Pseudo Statistic]

I know how to find that... but how do I find out how to get him to walk 300m along that line at 53 degrees? Like, how do I find out what angle he should be walking at instead? (To get him to be balanced at 53 degrees...)

 

[whozum]

Then instead of letting the net vector be the unknown, let his velocity be unknown. You know the wind vector, and you know the final vector you want, so subtract the wind from the final to get the man's.

[itex]v_{net} = v_{man} + v_{wind} [/tex]<br /> [itex]v_{man} = v_{net} - v_{wind} [/tex][/itex][/itex]