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Math Help - First time with vectors

  1. #1
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    First time with vectors

    Hello everyone,

    My name is Alex! I am taking the class algebra 2/ trigonometry honors! I have just finished the algebra 2 section of the class and am moving onto the trigonometry section of the class! Will any of you fine gentlemen be so kind as to help a child like myself with a few simple math problems I cannot understand? Thank you in advance!

    12. A force of 176 lbs. Makes an angle of 78°50’ with a second force. The resultant of the two forces makes an angle of 41°10’ with the first force. Find the magnitude of the second force and the resultant.
    __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ ____________________
    13. A force of 28.7 lbs. makes an angle of 42°10’ with a second force. The resultant of the two forces makes an angle of 32°40’ with the first force. Find the magnitude of the resultant.
    __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ ____________________
    14. A crate is supported by two ropes. One rope makes an angle of 46°20’with horizontal and has a tension of
    89.6 lbs. on it. The other rope is horizontal. Find the weight of the crate and the tension in the horizontal
    rope.
    __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ ____________________
    15. Two people are carrying a box, one on each side of the box. One person exerts a force of 150 lbs. at an
    angle of 62.4° with horizontal. The other person exerts a force 114 lbs. at an angle of 54.9°with horizontal.
    Find the weight of the box.




    I have the answers to the questions above but I do not understand how to get them! Please show work if you can! Thanks again!
    12. F2:189.59 lbs, r: 282.57 lbs.



    13. 116.73 lbs


    14. W: 64.8 lbs T: 61.9 lbs


    15. 226.2 lbs



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  2. #2
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    Re: First time with vectors

    12. A force of 176 lbs. Makes an angle of 78°50’ with a second force. The resultant of the two forces makes an angle of 41°10’ with the first force. Find the magnitude of the second force and the resultant.
    first off, it really helps to make a sketch when solving problems using vectors.

    use a coordinate system to your advantage ... let the first force, F_1 = 176 \, lbs , point along the (+) x-axis.

    let the second force have magnitude F_2 ... its direction will be 78°50’ relative to the (+) x-axis

    let the resultant have magnitude R ... its direction will be 41°10’ relative to the (+) x-axis



    in the x direction ...

    176 + F_2 \cos(78^\circ 50') = R\cos(41^\circ 10')

    in the y-direction ...

    F_2 \sin(78^\circ 50') = R\sin(41^\circ 10')


    using the second equation, solve for F_2 ...

    F_2 = \frac{R\sin(41^\circ 10')}{\sin(78^\circ 50')}

    substitute this expression for F_2 in the first equation ...

    176 + \frac{R\sin(41^\circ 10')\cos(78^\circ 50')}{\sin(78^\circ 50')}= R\cos(41^\circ 10')

    176 = R\cos(41^\circ 10') - \frac{R\sin(41^\circ 10')\cos(78^\circ 50')}{\sin(78^\circ 50')}

    176 = R\left[\cos(41^\circ 10') - \frac{\sin(41^\circ 10')\cos(78^\circ 50')}{\sin(78^\circ 50')}\right]

    \frac{176}{\cos(41^\circ 10') - \frac{\sin(41^\circ 10')\cos(78^\circ 50')}{\sin(78^\circ 50')}} = R

    I get |R| = 286.1 \, lbs and F_2 = 191.9 \, lbs

    I expect round-off error on the part of whoever came up with the provided solutions ... I did not round off in any step of my calculations.
    Thanks from alexster
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