Vector problem involving velocity and wind

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    Vector Velocity Wind
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SUMMARY

The discussion centers on a vector problem involving a 100-meter dash with a runner's velocity vector \(\vec{v} = 2\vec{e_{1}} + 6\vec{e_{2}}\) and a wind velocity vector \(\vec{w} = 5\vec{e_{1}} + \vec{e_{2}}\) km/h. The legal wind speed limit in the direction of the dash is 5 km/h. To determine if the race results will be disqualified, one must calculate the component of the wind velocity in the direction of the runner's velocity and compare its magnitude to the legal limit. The wind's projection onto the runner's direction must not exceed 5 km/h for the race to remain valid.

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braindead101
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A 100-meter dash is run on a track in the direction of [tex]\vec{v} = 2\vec{e_{1}}+6\vec{e_{2}}[/tex]. The wind velocity [tex]\vec{w}[/tex] is 5[tex]\vec{e}_{1}+\vec{e_{2}}[/tex] km/h. The rules say that a legal wind speed measured in the direction of the dash must not exceed 5 km/h. Will the race results be disqualified due to an illegal wind?

I am unsure how to start this problem, any help would be great. I think that I must find the speed of the wind in that direction first, so finding that vector and then finding the magnitude of that vector. But I don't know how to find that vector.
 
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If the wind speed is 5 km/h in any given direction, then it has to be less in a particular direction. So it cannot exceed 5 km/h in the track's direction.
 

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