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Math Help - Vectors+Tug Boat

  1. #1
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    Exclamation Vectors+Tug Boat

    Hey Everyone,
    I also need help on this one...quickly

    Dear Yahoo Answers,



    Two Tugboats are guiding a ship into Fremantle harbor. The force and direction of each of the tug boats and that applied by the ships own motor are given in the diagram below.



    1. Find the combined force of the two tug boats on the ship, giving your answer as a magnitude and direction ( Show Full Working)

    2. What is the total effective force on the boat when the force of the boat’s own motor is also taken into account. Give your answer in component form to 2dp.

    3. At what angle( to the vertical) will the boat be approaching the harbor wall?




    Please Help....Any contribution will be greatly, greatly appreciated.

    Thankyou
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  2. #2
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    I've attached a sketch of the forces.

    The red force is the combination of the 2 tugs.

    The blue force is the resulting force of all 3 forces.

    To calculate: Use Cosine rule in the painted triangle. Afterwards use a triangle containing the force caused by the ship's motor.
    Attached Thumbnails Attached Thumbnails Vectors+Tug Boat-bootankai.gif  
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  3. #3
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    Arrow Hmmmmmmmmmm

    Thankyou SOOOOO MUCH earboth......but after looking at my workbook throughly I was able to find out how they finish a similar problem....so i tried it out.

    Please see if it is correct....

    Two Tugboats are guiding a ship into Fremantle harbor. The force and direction of each of the tug boats and that applied by the ships own motor are given in the diagram below.



    1. Find the combined force of the two tug boats on the ship, giving your answer as a magnitude and direction ( Show Full Working)

    Tug (1) (4000 cos 10 i ) + ( 4000 sin 10 j) N
    Tug (2) (1500 cos 40 i) + ( -1500 sin 40 j ) N

    Therefore

    (4000 cos 10 + 1500 cos 40 ) i + ( 4000 sin 10 -1500 sin 40 ) j N

    5088 i - 269 j

    Magnitude = 5095 N, in direction 93.03 Degrees

    Please Evaluate and Check then I will proceed further.


    2. What is the total effective force on the boat when the force of the boat’s own motor is also taken into account. Give your answer in component form to 2dp.

    3. At what angle( to the vertical) will the boat be approaching the harbor wall?
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  4. #4
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    Quote Originally Posted by Pandp77 View Post
    ... 1. Find the combined force of the two tug boats on the ship, giving your answer as a magnitude and direction ( Show Full Working)

    Tug (1) (4000 cos 10 i ) + ( 4000 sin 10 j) N
    Tug (2) (1500 cos 40 i) + ( -1500 sin 40 j ) N

    Therefore

    (4000 cos 10 + 1500 cos 40 ) i + ( 4000 sin 10 -1500 sin 40 ) j N

    5088 i - 269 [B]j ....... OK

    Magnitude = 5095 N, ....... OK
    in direction 93.03 Degrees ....... OK
    All results are correct!
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