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Math Help - speed vectors problem

  1. #1
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    speed vectors problem

    Plane A is flying at 400 mph in the northeast direction relative to the earth. Plane B is flying at 500 mph in the north direction relative to the earth. What is the speed of Plane B as observed from Plane A?

    the answer is 357 mph, but i do not understand how to find this.
    Last edited by algebra2; October 2nd 2008 at 05:14 PM.
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  2. #2
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    the relative velocity vector R goes from the head of vector A to the head of vector B ... in other words

    (vector A) + (motion vector of B relative to A) = vector B

    I assume you know how to add vectors graphically to get a picture of the situation.

    you can solve for the magnitude of relative motion vector by using the law of cosines ...

    R = \sqrt{400^2 + 500^2 - 2 \cdot 400 \cdot 500 \cdot \cos(45^{\circ})}
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  3. #3
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    Hi algebra 2

    Ive just finished a project with relative motion so happy to help,

    If you draw a diagram (with straight line motion a triangle diagram) things become a lot clearer,

    Plane A is travelling NorthEast (at an angle of 45 from horizontal), Plane B is travelling North (90 deg from horizontal) Draw these two velocities as vectors which both originate at the origin (the earth)

    The relative motion equation says:
    vB = vA + vB/A velocity of B = velocity of A + velocity of B relative to A

    we already know vB and vA so to find vB/A we just solve the resulting vector triangle, in this situation I used the cosine rule as we have 2 adjacent sides with a angle in between (45)

    vB/A^2 = vA^2 + VB^2 -2*vB*vA*cos 45
    Solving this you get an answer of 356.59mph - Hope that helps
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  4. #4
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    Plane A is flying Northeast, so that is N 45deg E.
    Plane B is flying North.

    From plane A, the northing velocity of plane B is diminished by the northing velocity of plane A.
    So, the relative northing velocity of plane B from plane A is
    500 -400cos(45deg) = 217.157 mph due North.

    From plane A, plane B appears to be flying with a westward velocity that is equal to the eastward velocity of plane A, so,
    400sin(45deg) = 282.843 mph due West

    Hence, the resultant velocity of plane B as seen from plane A is
    R = sqrt[(217.157)^2 +(282.843)^2]
    R = 356.59 mph
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