Results 1 to 7 of 7

Math Help - vectors again

  1. #1
    Member
    Joined
    Sep 2008
    Posts
    117

    vectors again

    < is angle symbol

    R is the resultant of the three forces A, B, and C, that is R = A+B+C If
    A=A< 210, B= 100<20, C= 100<120, and R= R<195, use the component method to determine A and R.

    ok so I broke them into components but have no idea how to find A and R..any help appreciated.

    Ax= A cos 30= -?
    Ay= A sin 30 = -?
    Bx = 100 cos 20 = 93.9
    By = 100 sin 20 = 34
    Cx=100 sin 30= -50
    Cy=100 cos 30= 86.6
    Rx = R sin 15
    Ry= R cos 15

    where to begin...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by ur5pointos2slo View Post
    < is angle symbol

    R is the resultant of the three forces A, B, and C, that is R = A+B+C If
    A=A< 210, B= 100<20, C= 100<120, and R= R<195, use the component method to determine A and R.
    A\cos(210) + 100\cos(20) + 100\cos(120) = R\cos(195)

    R = \frac{A\cos(210) + 100\cos(20) + 100\cos(120)}{\cos(195)}


    A\sin(210) + 100\sin(20) + 100\sin(120) = R\sin(195)

    R = \frac{A\sin(210) + 100\sin(20) + 100\sin(120)}{\sin(195)}


    set the two expressions equal to R equal to each other and solve for A ... then find R.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2008
    Posts
    117
    Quote Originally Posted by skeeter View Post
    A\cos(210) + 100\cos(20) + 100\cos(120) = R\cos(195)

    R = \frac{A\cos(210) + 100\cos(20) + 100\cos(120)}{\cos(195)}


    A\sin(210) + 100\sin(20) + 100\sin(120) = R\sin(195)

    R = \frac{A\sin(210) + 100\sin(20) + 100\sin(120)}{\sin(195)}




    set the two expressions equal to R equal to each other and solve for A ... then find R.
    The solution always seems obvious after someone else does it. Thank you for your help again.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Jan 2009
    Posts
    591
    Quote Originally Posted by ur5pointos2slo View Post
    < is angle symbol

    R is the resultant of the three forces A, B, and C, that is R = A+B+C If
    A=A< 210, B= 100<20, C= 100<120, and R= R<195, use the component method to determine A and R.

    ok so I broke them into components but have no idea how to find A and R..any help appreciated.

    Ax= A cos 30= -?
    Ay= A sin 30 = -?
    Bx = 100 cos 20 = 93.9
    By = 100 sin 20 = 34
    Cx=100 sin 30= -50
    Cy=100 cos 30= 86.6
    Rx = R sin 15
    Ry= R cos 15

    where to begin...

    I do not like the reduction of angles,
    it is much too easy to lose the correct sign.


    Ax = A cos(210) ; Ay = A sin(210)
    Bx = 100 cos(020) ; By = 100 sin(020)
    Cx = 100 cos(120) ; Cy = 100 sin(120)
    ======================================
    Rx = R cos(195) ; Ry = R sin(195)


    2 equations, 2 unknowns

    -0.866 A + 93.969 -50.000 = -0.966 R
    &
    -0.500 A + 34.202 + 86.602 = -0.259 R

    reduced:
    -0.866 A + 43.969 = -0.966 R
    -0.500 A + 120.804 = -0.259 R
    &
    -0.259(-0.866 A + 43.969) = -0.966(-0.500 A + 120.804 )
    1 equation 1 unknown

    (my response was toooo slow, need more coffee)
    Last edited by aidan; September 7th 2009 at 09:26 AM. Reason: typo errors
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Sep 2008
    Posts
    117
    Quote Originally Posted by aidan View Post
    I do not like the reduction of angles,
    it is much too easy to lose the correct sign.


    Ax = A cos(210) ; Ay = A sin(210)
    Bx = 100 cos(020) ; By = 100 sin(020)
    Cx = 100 cos(120) ; Cy = 100 sin(120)
    ======================================
    Rx = R cos(195) ; Ry = R sin(195)


    2 equations, 2 unknowns

    -0.866 A + 93.969 -50.000 = -0.966 R
    &
    -0.500 A + 34.202 + 86.602 = -0.259 R

    reduced:
    -0.866 A + 43.969 = -0.966 R
    -0.500 A + 120.804 = -0.259 R
    &
    -0.259(-0.866 A + 43.969) = -0.966(-0.500 A + 120.804 )
    1 equation 1 unknown

    (my response was toooo slow, need more coffee)
    Thanks for your response though. They both were useful to me.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Sep 2008
    Posts
    117
    Quote Originally Posted by aidan View Post
    I do not like the reduction of angles,
    it is much too easy to lose the correct sign.


    Ax = A cos(210) ; Ay = A sin(210)
    Bx = 100 cos(020) ; By = 100 sin(020)
    Cx = 100 cos(120) ; Cy = 100 sin(120)
    ======================================
    Rx = R cos(195) ; Ry = R sin(195)


    2 equations, 2 unknowns

    -0.866 A + 93.969 -50.000 = -0.966 R
    &
    -0.500 A + 34.202 + 86.602 = -0.259 R

    reduced:
    -0.866 A + 43.969 = -0.966 R
    -0.500 A + 120.804 = -0.259 R
    &
    -0.259(-0.866 A + 43.969) = -0.966(-0.500 A + 120.804 )
    1 equation 1 unknown

    (my response was toooo slow, need more coffee)
    I do however think these are mixed up
    -0.866 A + 93.969 -50.000 = -0.966 R
    &
    -0.500 A + 34.202 + 86.602 = -0.259 R

    shouldnt it be

    -0.866 A + 93.969 -50.000 = -0.259 R
    &
    -0.500 A + 34.202 + 86.602 = -0.966 R

    or am i missing something
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Sep 2008
    Posts
    117
    I got A=15.8 but compared to the rest of the values in the problem this seems very small. Could someone please verify if this is the correct value for A.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: November 15th 2011, 05:10 PM
  2. Replies: 3
    Last Post: June 30th 2011, 08:05 PM
  3. Replies: 2
    Last Post: June 18th 2011, 10:31 AM
  4. [SOLVED] Vectors: Finding coefficients to scalars with given vectors.
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: January 23rd 2011, 12:47 AM
  5. Replies: 4
    Last Post: May 10th 2009, 06:03 PM

Search Tags


/mathhelpforum @mathhelpforum