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Math Help - Distance relative to direction?

  1. #1
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    Distance relative to direction?

    Not a homework problem if that's any consolation.

    My Father and I happened to be discussing time dilation. My analogy hit a bit of a snag when be disagree on some math.

    If I were traveling north at 10 miles an hour, I would be moving 10 mph north and 0 mph east, and if I were traveling 10 mph east I would be going 10 mph east and 0 mph north.

    But what about the Diagonal? My father said that traveling at the Diagonal at 10 would mean 5 each direction. I drew up a similar diagram to this.


    y is the distance in both directions, so solving for y would tell me how far in each direction I would travel.
    2y^2 = 100
    y^2 = 50
    y = 5\sqrt{2}

    He assures me I'm wrong, but I'm pretty sure I'm right. Who messed up here?
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  2. #2
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    You are right !
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  3. #3
    Member u2_wa's Avatar
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    exactly you are right
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  4. #4
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    So going x speed at a 45 degree angle I'm the sum of my speeds relative to the axis is greater than my speed ( x\sqrt5)
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