Vector addition is often illustrated graphically with a parallelogram diagram, as shown below.baabSuppose this diagram rolates to the vectors for Initial position, final position, and displacemont of an object in motion.Suppose the origin of coordinates is the lower-left coner of the parallelogram and that the initial position is shown by vector Then, thedisplacement vector could correspond to:a+b

initial position = a→final position = b→

Vector addition is often illustrated graphically with a parallelogram diagram, as shown below. a a b Suppose this diagram relates to the vectors for Initial position, final position, and displacement of an object in motion. Suppose the origin of coordinates is the lower-left comer of the parallelogram and that the initial position is shown by vector Then, the displacement vector could correspond to: a+b

Vector addition is often illustrated graphically with a parallelogram diagram, as shown below. a a b Suppose this diagram relates to the vectors for Initial position, final position, and displacement of an object in motion. Suppose the origin of coordinates is the lower-left comer of the parallelogram and that the initial position is shown by vector Then, the displacement vector could correspond to: a+b

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter2: Vectors

Section: Chapter Questions

Problem 41P: A trapper walks a 5.0-lan straight-line distance from her cabin to the lake, as shown in the...

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A trapper walks a 5.0-km straigt4ine distance from his cabin to the lake, as shown in the following figure. Use a graphical method (the parallelogram rule) to determine the trapper’s displacement directly to the east and displacement directly to the north that sum up to his resultant displacement vector. If the trapper walked only in directions east and north, zigzagging his way to the lake, how many kilometers would he have to walk to get to the lake?
A trapper walks a 5.0-lan straight-line distance from her cabin to the lake, as shown in the following figure. Determine the east and north components of her displacement vector. How many more kilometers would she have to walk if she walked along the component displacements? What is her displacement vector?
For the vectors given in the following figure, use a graphical method to find the following resultants: (a) A+B , (b) C+B , (c) D+F , (d) AB , (e) DF , (f) A+2F , (g) C+2D ; and (h) A4D+2F .
Given two displacement vectors A=(3.00i-4.00j-4.00K)m and B=(2.00i+3.00j-7.00K)m , find the displacements and their magnitudes for (a) C=A+B and (b) D=2AB .
For vectors and , calculate (a) and its magnitude and direction angle, and (b) and its magnitude and direction angle.
Assuming the +x-axis is horizontal to the right for the vectors in the preceding figure, find (a) the component of vector Aalong vector C , (b) the component of vector Calong vector A , (c) the component of vector i along vector F , and (d) the component of vector Falong vector i .
Check your Understanding A blue fly lands on a sheet of graph paper a point located 10.0 cm to the right of its left edge and 8.0 cm above its bottom edge and walks slowly to a point located 5.0 cm from the left edge and 5.0 cm from the bottom edge. Choose the rectangular coordinate system with the origin at the lower left-side comet of the paper and find the displacement vector of the fly. Illustrate your solution by graphing.
Check Your Understanding For the vectors given in Figure 2.13, find the scalar products AB and CF . The three displacement vectors A , B , and C in Figure 2.13 are specified by their magnitudes A=10.0,B=7.0 and C=8.0 , respectively, and by their respective direction angles with the horizontal direction =35,=110 , and =30 . The physical units of the magnitudes are centimeters. Choose a convenient scale and use a ruler and a protractor to find the following vector sums: (a) R=A+B , (b) D=AB , and (c) S=A3B+C .
Consider the three displacement vectors A=(3i3j)m, B=(i4j)m, and C=(2i+5j)m. Use the component method to determine (a) the magnitude and direction of the vector D=A+B+C and (b) the magnitude and direction of E=AB+C.
Assuming the +x -axis is horizontal to the right for the vectors given in the following figure, use the analytical method to find the following resultants: (a) A+B , (b) C+B , (c) D+F , (d) AB , (e) DF , (f) A2F , (g) C2D+3F , and (h) A4D+2F .
A fly enters through an open window and zooms around the room. In a Cartesian coordinate system with three axes along three edges of the room, the fly changes its position from point b(4.0m,1.5m,2.5m) to point e(1.0m,4.5in,0.5m) . Find the scalar components of the fly’s displacement vector and express its displacement vector in vector component form. What is its magnitude?
The following figure shows a triangle formed by the three vectors A , B , and C . If vector C is drawn between the midpoints of vectors A and B , show that C=C/2