Results 1 to 2 of 2

Math Help - boat in water, force vectors

  1. #1
    Member
    Joined
    Nov 2006
    From
    chicago
    Posts
    156

    boat in water, force vectors

    A boat heads in the direction N 40 degrees W at a speed of 24 knots. The current runs at 6 knots in the direction N 25 degrees E. Find the resultant speed and direction of the boat.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,914
    Thanks
    779
    Hello, Mr_Green!

    I must assume you are familiar with vectors.


    A boat heads in the direction N 40░ W at a speed of 24 knots.
    The current runs at 6 knots in the direction N 25░ E.
    Find the resultant speed and direction of the boat.
    Code:
                E  6Ěsin25░ C
                + - - - - - *
                :         /
       6Ěcos25░ :       / 6
                :     /
                :25░/
                : /  24Ěsin24░
              B * - - - - - - + D
                  \           :
                    \         :
                      \       : 24Ěcos24░
                    24  \     :
                          \40░:
                            \ :
                              *
                              A

    The boat is moving from point A to point B.
    . . Its horizontal component is: DB = -24Ěsin24░
    . . Its vertical component is: AD = 24Ěcos24░

    The current is moving from point B to point C.
    . . Its horizontal component is: EC = 6Ěsin25░
    . . Its vertical component is: BE = 6Ěcos25░

    The resultant vector is AC.
    We must determine its magnitude and direction.


    The horizontal component of AC is: .-24Ěsin24░ + 6Ěsin25░ . .-7.226
    The vertical component of AC is: .24Ěcos24░ + 6Ěcos25░ . .27.363
    . . . . . . . . . . . . . . . . . . . . . ________________
    The magnitude is: .|AC| .= .√(-7.226)▓ + 27.363▓ .= .28.30103965

    . . Therefore, the speed of the boat is about 28.3 knots.


    The direction angle is given by: .tanθ .= .7.226/27.363 . . θ .= .14.79292136░

    . . Therefore, the direction is about: .N 14.8░ W

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: January 31st 2011, 06:12 AM
  2. Speed of Boat in Still Water
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: December 4th 2008, 08:16 PM
  3. Boat in Still Water
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: November 28th 2008, 04:15 PM
  4. Boat in Still Water
    Posted in the Algebra Forum
    Replies: 4
    Last Post: November 28th 2008, 10:08 AM
  5. Speed of the Boat in Still Water
    Posted in the Algebra Forum
    Replies: 4
    Last Post: November 19th 2008, 04:37 PM

Search Tags


/mathhelpforum @mathhelpforum