Resolving a vector into components is like the parallelogram or head-to-tail method in reverse. Consider the following example. Given vector R: R, and R, are the x and y (scalar) components of R. Rj Note: The vector notati on for the scalar components is dropped. However, the vector may be expressedin vector components or scal ar components with unit vectors RR, +R, -R,i +RJ In determining the x and y components of vector R, you are looking for vectors along the x and y axes that add up to produce R. Sumply draw a rectangle (a special case of a parallelogram) to determine Ra and R, Note that above both components are positive since both point along the positive x and y axes. 1. Sketch the x and y components of d A, is positive / negative A, is positive/ negative With a little right triangle trigonometry, component values can be determined The basic trironometric relationships are shown

Resolving a vector into components is like the parallelogram or head-to-tail method in reverse. Consider the following example. Given vector R: R, and R, are the x and y (scalar) components of R. Rj Note: The vector notati on for the scalar components is dropped. However, the vector may be expressedin vector components or scal ar components with unit vectors RR, +R, -R,i +RJ In determining the x and y components of vector R, you are looking for vectors along the x and y axes that add up to produce R. Sumply draw a rectangle (a special case of a parallelogram) to determine Ra and R, Note that above both components are positive since both point along the positive x and y axes. 1. Sketch the x and y components of d A, is positive / negative A, is positive/ negative With a little right triangle trigonometry, component values can be determined The basic trironometric relationships are shown

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 2.3CYU: Check Your understanding Using the three displacement vectors A , B , and F in Figure 2.13, choose a...

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Check Your Understanding Verify that vector v V obtained in Example 2.14 is indeed a unit vector by computing its magnitude. If the convoy in Example 2.8 was moving across a desert flatland—that is, it the third component of its velocity was zero—what is the unit vector of its direction of motion? Which geographic direction does it represent?
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 .
Suppose you walk 18.0 m straight west and then 25.0 m straight north. How far are you from your starting point? What is your displacement vector? What is the direction of your displacement? Assume the +x -axis is horizontal to the right.
Assuming the +x-axis is horizontal to the right for the vectors in the previous figure, find the following vector products: AC , (b) AF , (c) DC , (d) A(F+2C) , (e) iB , (f) jB , (g)
Find the angles that vector makes with the and axes.
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 .
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 .
A small plane flies 40.0 km ma direction 60 north of east and then flies 30.0 km in a direction 15 north of east. Use the analytical method to find the total distance the plane covers from the starting point, and the geographic direction of its displacement vector. What is its displacement vector?
A skater glides along a circular path of radius 5.00 m in clockwise direction. ‘When he coasts around one- half of the circle, starting from the west point, find (a) the magnitude of his displacement vector and (b) how far he actually skated. (c) What is the magnitude of his displacement vector when he skates all the way around the circle and comes back to the west point?
Assuming the +x -axis is horizontal and points to the tight, resolve the vectors given In the following figure to their scalar components and express them in vector component form.
For the three-dimensional vectors in the following figure, find (a) GH , (b) GH , and (c) GH .
If vectors A and B are orthogonal, what is the component of B along the direction of A ? What Is the component of A along the direction of B ?