Bob is a vector with magnitude 240 and direction 200 degrees. Mai is a vector of length 160 @ 310 degrees. Jose is a vector of 210 @ 170 degrees. Calculate the following vectors and report their magnitude and angle (measured counterclockwise from the positive x-axis):
(a) Bob + Mai
(b) Mai – Bob
(c) Jose + Bob – Mai
Comment: "If possible. I'd like to know the how and why on some steps, please. Thanks"
Given : Bob : 240@200° , Mai: 160@310° , Jose: 210@170°
Solution:
(a) Bob + Mai
Components of vector Bob : Bobx = 240cos(200)= -225.53
Boby= 240sin(200) = -82.08
Components of vector Mai: Maix = 160cos(310)= 102.85
Maiy = 160sin(310)= -122.57
Vector addition in x direction :
Bobx+Maix = -225.53 +102.85 = -122.68
Vector addition in y direction:
Boby +Maiy = -82.08 -122.57 = -204.65
Magnitude of vector addition |Bob +Mai| is given by:
[(-122.68)2+(-204.65)2]
= 238.60
Direction of vector addition is given by:
=
tan-1(-204.65/-122.68) = 59.06°
Hence
Bob + Mai = 238.60 @ 59.06°
(b) Mai - Bob
Vector subtraction in x direction:
Maix - Bobx = 102.85 -(-225.53) = 328.38
Vector subtraction in y direction:
Maiy - Boby = -122.57 -(-82.08) = -40.49
Magnitude of vector subtraction (|Mai - Bob|) is given by:
[(328.38)2+(-40.49)2]
= 330.87
Direction of vector subtraction is given by:
=
tan-1(-40.49/328.38) = -7.02° (clockwise)
= 360-7.02=
352.97° (anticlockwise)
Hence
Mai - Bob = [email protected]°
(c) Jose + Bob - Mai
Vector components of Jose : Josex = 210cos(170)= -206.81
Josey = 210sin(170)= 36.47
X direction:
Josex+Bobx-Maix = -206.81 -225.53 -102.85 = -121.57
y direction:
Josey+Boby-Maiy= 36.47-82.08-(-122.57) = 76.96
Magnitude | Jose+Bob-Mai| is given by:
[(-122.57)2+(76.96)2]
= 144.73
Its direction is given by:
=
tan-1(76.96/-121.57) = -32.34° (clockwise)
= 360°-32.34° =
327.66° (anticlockwise)
Hence
Jose + Bob - Mai = 144.73@ 327.66°
Bob is a vector with magnitude 240 and direction 200 degrees. Mai is a vector of...
Bob is a vector with magnitude 240 and direction 200 degrees. Mai is a vector of length 160 @ 310 degrees. Jose is a vector of 210 @ 170 degrees. Calculate the following vectors and report their magnitude and angle (measured counterclockwise from the positive x-axis): Bob + Mai Mai - Bob Jose + Bob - Mai Comment: "Please, if possible, I'd like to see steps, thanks. Also, do I need to use graphs for this kind of problem?"
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