Problem 3.22 The figure (figure 1) shows vectors A vector and B vector. Let C ve

Question

Problem 3.22 The figure (figure 1) shows vectors A vector and B vector. Let C vector = A vector + B vector. Based on the figure, use geometry and trigonometry to calculate the magnitude of C. Part C Based on the figure, use geometry and trigonometry to calculate the direction of C vector. Measure angles counterclockwise from the x-axis Part D Decompose vectors A and B into components. then use these to calculate algebraically the components of C vector. Enter your answers numerically separated by a comma.

Explanation / Answer

a) Guide to Drawing Vector C
    Draw Vector A as it is.
Draw Vector B such that tail of Vector B is coinciding with Tip of Vector A.
Now Join, tail of Vector A , with Tip of Vector B , the resultant Vector = Vector C

   Please let me know in case you need me to draw the same.

b)
A = 3* cos(20) i + 3 * sin(20) j
B = 2 * cos(60) i + 2 * sin(60) j

C = A+B
C = (3* cos(20) + 2 * cos(60)) i + ( 3 * sin(20) + 2 * sin(60)) j
C = 3.82 i + 2.76 j

Magnitude of C = sqrt( 3.82^2 + 2.76^2 )
Magnitude of C = 4.71

Direction of C = = tan^-1(2.76/3.82)
= 35.85o from +ve Xaxis in Anti clockwise Direction.

A = 3* cos(20) i + 3 * sin(20) j
A = 2.82 i + 1.03 j
B = 2 * cos(60) i + 2 * sin(60) j =
B = i + 1.73 j

C = 3.82 i + 2.76 j

Cx = 3.82
Cy = 2.76

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