Vector problem involving velocity and wind

1. Sep 20, 2007

A 100-meter dash is run on a track in the direction of $$\vec{v} = 2\vec{e_{1}}+6\vec{e_{2}}$$ . The wind velocity $$\vec{e}_{1}+\vec{e_{2}}$$ km/h. The rules say that a legal wind speed measured in teh 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.

2. Sep 20, 2007

is the answer just projecting wind onto the velocity .
proj v (w) = (w, v / v,v )v
= ([5 1],[2 6] /[2 6],[2 6])[2 6]
= ((10+6)/(4+36))[2 6]
= 16/40 [2 6]
= [4/5 12/5]

so magnitude of that is around 2.52, so no the race won't be disqualified... am i doing somethin wrong. and should the 100-meter be incorporated somehow?

3. Sep 20, 2007

HallsofIvy

Staff Emeritus
No, the condition under which the race is disqualified says nothing about the length of the race, only the speed of the wind. Taking the projection of the wind vector onto the direction of the race is exactly right.