phy111

A truck is moving at a speed of 70km/h. The exhaust pipe above the truck cab sends out a trail of smoke that makes an angle of
20o
east of south behind the truck. If the wind is blowing directly toward the east, what is the wind speed at that location?

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  1. In what direction is the truck moving, due south, south-west?
    Answers will vary depending on the direction.

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  2. is not given in the question

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  3. We assume that the wind is blowing east at x km/h, represented by the vector <x,0>
    The truck is moving along the vector <p,q>, where sqrt(p²+q²)=70 km/h, or <sqrt(70²-q²), q>
    We also know that the resultant of the two velocities equals <u,v> where
    tan(-70°)=u/v.

    Combining all information, we have:
    resultant velocity of smoke
    =<u,v>
    =<x,0>+<sqrt(70²-q², q)
    =<x+sqrt(70²-q²), q>
    where
    tan(-70°)=u/v
    =(x+sqrt(70²-q²)) / q

    Solve for x when q is known.

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  4. 25.4779

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  5. A truck is moving north at speed of 70km/h. The exhaust pipe above the truck cab sends out a trail of smoke that make an angle of 20degree east of south behind the truck. If the wind os blowing directly towards the east what is the wind speed at that location

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