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Math Help - Relative Velocities

  1. #1
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    Talking Relative Velocities

    The question reads:

    "A glider is moving with a velocity  v = (40, 30, 10) relative to the air and is blown by the wind which has velocity relative to the earth of  w = (5, -10, 0) . Find the velocity of the glider relative to the earth."

    My argument goes that as the velocity of the wind relative to the earth increases, and the velocity of the glider relative to the air, increase, so does the velocity of the glider relative to earth. So if we let  v_E represent the velocity of the glider relative to the earth,

     v_E = v + w .

    Therefore, in this case the velocity of the glider relative to the earth,

     v_E = (40, 30, 10) + (5, -10, 0) = (45, 20, 10)

    However, the answer booklet has the expression for  v_E as follows:

     v_E = v - w

    giving  v_E = (35, 40, 10) which I suppose must be the right answer. Could somebody explain this result to me? Thank you.
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  2. #2
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    Quote Originally Posted by Harry1W View Post
    The question reads:

    "A glider is moving with a velocity  v = (40, 30, 10) relative to the air and is blown by the wind which has velocity relative to the earth of  w = (5, -10, 0) . Find the velocity of the glider relative to the earth."

    My argument goes that as the velocity of the wind relative to the earth increases, and the velocity of the glider relative to the air, increase, so does the velocity of the glider relative to earth. So if we let  v_E represent the velocity of the glider relative to the earth,

     v_E = v + w .

    Therefore, in this case the velocity of the glider relative to the earth,

     v_E = (40, 30, 10) + (5, -10, 0) = (45, 20, 10)

    However, the answer booklet has the expression for  v_E as follows:

     v_E = v - w

    giving  v_E = (35, 40, 10) which I suppose must be the right answer. Could somebody explain this result to me? Thank you.
    I agree with you ... (air vector) + (wind vector) = ground vector

    the answer booklet is in error, imho.
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  3. #3
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    Hello Harry1W
    Quote Originally Posted by Harry1W View Post
    The question reads:

    "A glider is moving with a velocity  v = (40, 30, 10) relative to the air and is blown by the wind which has velocity relative to the earth of  w = (5, -10, 0) . Find the velocity of the glider relative to the earth."

    My argument goes that as the velocity of the wind relative to the earth increases, and the velocity of the glider relative to the air, increase, so does the velocity of the glider relative to earth. So if we let  v_E represent the velocity of the glider relative to the earth,

     v_E = v + w .

    Therefore, in this case the velocity of the glider relative to the earth,

     v_E = (40, 30, 10) + (5, -10, 0) = (45, 20, 10)

    However, the answer booklet has the expression for  v_E as follows:

     v_E = v - w

    giving  v_E = (35, 40, 10) which I suppose must be the right answer. Could somebody explain this result to me? Thank you.
    You need to check on the definition of 'wind velocity'. Sometimes (perversely!) it's given as the direction from which the wind blows. For example, a north-easterly is a wind that blows from the N-E; i.e towards the South-West.

    This would indeed make the velocity of the glider relative to the earth v - w.

    Grandad
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  4. #4
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    Quote Originally Posted by Grandad View Post
    Hello Harry1WYou need to check on the definition of 'wind velocity'. Sometimes (perversely!) it's given as the direction from which the wind blows. For example, a north-easterly is a wind that blows from the N-E; i.e towards the South-West.

    This would indeed make the velocity of the glider relative to the earth v - w.

    Grandad
    I thought about that also, but dismissed it since the wind was given in proper vector notation.
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