Question

1. Vector addition and subtraction: We are given the magnitudes and directions of the vectors A and B as follows (a) Carefully sketch each vector individually, then sketch the sum C-A+B and sketch the difference D-A B. Try to make the lengths to scale and make the angles relatively accurate. (Use a protractor.) Use trigonometry to find the components of cach of the four vectors A, B, C, and D Use trigonometry to find the directions of Cand D (b) 2. More Vector Arithmetic Consider the following dimensionless vectors: Vector A has length 100 and points along a direction 30° counter-clockwise from the positive r axis. Vector B has length 200 and points along a direction 20° clockwise from the positive r axis. Vector C has length 75 and points along a direction 40° counter-clockwise from the positive y axis. (a) Carefully sketch the x and y axes and add the vectors A, B, and C. The vectors in your sketch should have approximately the correct length and orientation. (b) Find the components of A, B, and C. (c) Define a fourth vector D-A -C Use a graphical method to estimate the length and orientation of D (d)Use an algebraic method to find the length and orientation of D 3. Addition of Vectors A 50 m I'hree displacement vectors have the magnitudes and orientations shown in the figure 50° 60° B- 100 m C- 30 m (a) Find the x and y components of each of the three vectors (b) Find the sum of the 3 vectors graphically. Make a neat drawing (c) Find the components, magnitude, and orientation of the sum of the three vectors

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Answer 1

vectors: C vector = A vector + B vector D vector = A vector - B vector Components: A vector: A_x = A cos 40 degree = 3.83' A_y = A sin 40 degree 3.21 B vector: B-x = B cos 170 degree = -2.95: B_y = B sin 170 degree = 0.52 C vector: C_x = A_x + B_x = 0.88: C_y = A_y + B_y = 3.73 D vector: D_x = A_x - B_x = 6.78: D_y = A_y - B_y = 2.69 \r\n Vertical-bar A vector Vertical-bar = 100 Vertical-bar B vector Vertical-bar = 200 Vertical-bar C vector Vertical-bar = 75 Components A vector: A_x = A cos 30 degree = 86.60: A_y = A sin 30 degree = 50 B vector: B_x = B cos 20 degree = 187.93: B_y = -B sin 20 degree = -68.40 C vector: C_x = C sin 40 degree = 48.20: C_y = C cos 40 degree = 57.45