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    Vectors and force: Speed of car in wind

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    I wanted some help w/ a vector hypothetical. Say, there's is a wind, coming from the northwest (and going southeast), blowing at 25 to 30 MPH on a vehicle traveling east at 55MPH, say at 30 degree to the vehicle, a positive force on the back and left side of this vehicle. What formula would you use to should this positive force? Plus, if this vehicle averaged approximately 30 MPG, can we expect a slight increase in fuel ecomony -- perhaps pushing the fuel ecomony to 32 MPG -- can we come up w/ some numbers/formula to show this increase?

    Again, this is a hypothetical as far as vectors go, so we have some liberties here. Try to stick w/ formulas connected to vectors. The mass of the vehicle is approx. 2250 lbs. The angle of the wind/air is 30 degrees to the vehicle, but we can say the angle of the turning air runs from 60 to 210 degrees, depending on location -- I'll leave it up to you as which one you want to go with. Nevertheless, I would like to go with a relatively straight forward (if possible) somewhat "simple" formula and/or explanation.

    Let's also say that 55 MPH is w/out the wind, otherwise a slight increase in MPH can be expected w/ the wind. We know that the wind can be unreliable, unpredictable, but again we'll just pick one moment in time to make this analysis.

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    Solution Preview

    Please see the attached file.

    According to the problem we can draw a force diagram as shown above. Fw means the force from wind applies to the car, Fwy is its y component (Fwy = Fw*sin(Θ ) perpendicular to the movement of the ...

    Solution Summary

    The explanation is detailed and complete with formulas and conclusions.