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Math Help - Vectors

  1. #1
    Member classicstrings's Avatar
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    Vectors

    Thanks, I am having a little trouble...

    1.A ship is travelling @ 12 m/s. A passenger walks towards the back at 5 m/s. After walking for 2 sec, he then walks at the same speed at right angles to the direction of the ship for 2 secs.

    Relative to the water:

    a. What is the velocity in each case
    b. What is the displacement in each case

    2.A ship travelling @ 46km/hr aiming at the direction 124 T is pulled off course by a current of 8 km/hr in the direction 223 T. Find actual speed and direction of ship.

    THanks for the help!
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  2. #2
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by classicstrings
    Thanks, I am having a little trouble...

    1.A ship is travelling @ 12 m/s. A passenger walks towards the back at 5 m/s. After walking for 2 sec, he then walks at the same speed at right angles to the direction of the ship for 2 secs.

    Relative to the water:

    a. What is the velocity in each case
    b. What is the displacement in each case
    (I'm not sure if you want it written in terms of i j and k but i'll do it anyway)
    a. the boat is moving with a vector of 12\bold{i}
    the man is moving with a vector of \neg5\bold{i}
    therefore the vector that shows his movemant relative to the water is:

    12\bold{i}+\neg5\bold{i}=12\bold{i}-5\bold{i}=\boxed{7\bold{i}}

    therefore his velocity is 7m/s

    therefore his displacement after 2 sec is... 7\times2=14 metres

    b.the boat is moving with a vector of 12\bold{i}+0\bold{j}
    the man is moving with a vector of 0\bold{i}+5\bold{j}
    therefore the vector that shows his movemant relative to the water is:

    12\bold{i}+5\bold{j}

    therefore his velocity is...
    v=\sqrt{12^2+5^2}

    v=\sqrt{144+25}

    v=\sqrt{169}

    \boxed{v=13}m/s

    therefore his displacement after 2 sec is... 13\times2=26 metres

    ~ Q\!u\!i\!c\!k
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  3. #3
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    A question of my own

    Quote Originally Posted by classicstrings
    2.A ship travelling @ 46km/hr aiming at the direction 124 T is pulled off course by a current of 8 km/hr in the direction 223 T. Find actual speed and direction of ship.
    What is "T"
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  4. #4
    Member classicstrings's Avatar
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    I meant degrees true, but thanks I have worked out the 2nd one. Cheers!
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