Explore BrainMass

Explore BrainMass

    Vector

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    1) A team of surveyors mark off distances represented by vectors of (85m, 55 degrees), (43m, 0 degrees) and (37m, 345 degrees). Solve for the resultant displacement.

    2) Find the resultant force. (463 N, 137 degrees), (258 N, 268 degrees) and (379 N, 128 degrees)

    © BrainMass Inc. brainmass.com December 24, 2021, 5:08 pm ad1c9bdddf
    https://brainmass.com/math/basic-algebra/solve-resultant-displacement-31041

    SOLUTION This solution is FREE courtesy of BrainMass!

    A team of surveyors mark off distances represented by vectors of (85m, 55 degrees), (43m,0 degrees)and (37m,345 degrees). Solve for the resultant displacement.

    Component is the horizontal (x) direction = (Magnitude) x (Cos phi )
    Component is the vertical (y) direction = (Magnitude) x (Sin phi )

    a) (85m, 55 degrees)
    Magnitude = 85 m
    phi = 55 degrees
    x component = 48.75 m =85 Cos55
    y component = 69.63 m =85 Sin55

    b) (43m,0 degrees)
    Magnitude = 43 m
    phi = 0 degrees
    x component = 43 m =43 Cos0
    y component = 0 m =43 Sin0

    c) (37m, 345 degrees)
    Magnitude = 37 m
    phi = 345 degrees
    x component = 35.74 m =37 Cos345
    y component = -9.58 m =37 Sin345

    Total displacement in x direction= 127.49 m =48.75+43+35.74
    Total displacement in y direction= 60.05 m =69.63+0+-9.58

    Resultant displacement = square root of {(x component) ^2 + (y component)^2}= 140.92 m =square root of (127.49^2+60.05^2)

    Angle between the resultant and x axis = tan inverse ( y component / x component)

    25.22 degrees = tan inverse (60.05/127.49)

    Answer:
    Resultant displacement = 140.92 m at an angle of 25.22 degrees from x axis
    0r (140.92m, 25.22degrees)

    Qn 2) Find the resultant forces. (463 N,137 degrees),(258 N,268 degrees) and (379 N 128 degrees)

    Component is the horizontal (x) direction = (Magnitude) x (Cos phi )
    Component is the vertical (y) direction = (Magnitude) x (Sin phi )

    a) (463N, 137 DEGREES)
    Magnitude = 463 N
    phi = 137 degrees
    x component = -338.62 N =463 Cos137
    y component = 315.77 N =463 Sin137

    b) (258 N, 268 DEGREES)
    Magnitude = 258 N
    phi = 268 degrees
    x component = -9.00 N =258 Cos268
    y component = -257.84 N =258 Sin268

    c) (379 N 128 DEGREES)
    Magnitude = 379 N
    phi = 128 degrees
    x component = -233.34 N =379 Cos128
    y component = 298.66 N =379 Sin128

    Total force in x direction= -580.96 N =-338.62+-9+-233.34
    Total force in y direction= 356.59 N =315.77+-257.84+298.66

    Resultant force = square root of {(x component)^2 + (y component)^2}= 681.67 m =square root of (-580.96^2+356.59^2)

    Angle between the resultant and x axis = tan inverse ( y component / x component)

    -31.54 degrees = tan inverse (356.59/-580.96)
    or 148.46 degrees =180-31.54
    Answer:
    Resultant force = 681.67 N at an angle of 148.46 degrees from x axis
    0r (681.67N,148.46 degrees)

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 5:08 pm ad1c9bdddf>
    https://brainmass.com/math/basic-algebra/solve-resultant-displacement-31041

    Attachments

    ADVERTISEMENT