tor math.pdf In parts d, e, and f, we will redo the previous calculations using component methods. (d) Using trigonometry, calculate the x and y components of the vectors A and B. Note: do not make measurements of your graph paper drawings. Part d should be pure calculator work. x-component of A: A, = y-component of A: A, = x-component of B: B = y-component of B: B, = (e) Using your components from part d above, calculate the x and y components of R. S, and D. Remember, R=A+B, S = A + 2B, and D=B-A. x-component of R: R₁ = y-component of R: R, = x-component of S: S, = y-component of S: S, = X-component of D: D. = y-component of D: D, =

tor math.pdf In parts d, e, and f, we will redo the previous calculations using component methods. (d) Using trigonometry, calculate the x and y components of the vectors A and B. Note: do not make measurements of your graph paper drawings. Part d should be pure calculator work. x-component of A: A, = y-component of A: A, = x-component of B: B = y-component of B: B, = (e) Using your components from part d above, calculate the x and y components of R. S, and D. Remember, R=A+B, S = A + 2B, and D=B-A. x-component of R: R₁ = y-component of R: R, = x-component of S: S, = y-component of S: S, = X-component of D: D. = y-component of D: D, =

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 46P: A fly enters through an open window and zooms around the room. In a Cartesian coordinate system with...

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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 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 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?
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?
For the three-dimensional vectors in the following figure, find (a) GH , (b) GH , and (c) GH .
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)
between points in a plane do not change when a coordinate system is rotated In other words, the magnitude of a vector Is invariant under rotations of the coordinate system. Suppose a coordinate system S is rotated about its origin by angle to become a new coordinate system S’, as shown in the following figure. A point in a plane has coordinates (x,y)in S and coordinates (x,y) in S’. (a) Show that, during the transformation of rotation, the coordinates in S are expressed in terms of the coordinates in S by the following relations: {x=xcos+ysiny=xsin+ycos (b) Show that the distance of point Pto the origin is invariant under rotations of the coordinate system. Here, you have to show that x2+y2=x2+y2. (c) Show that the distance between points Pand Q is invariant under rotations of the coordinate system. Here, you have to show that ( xP =xQ )2+( yP yQ )2=( xP =xQ )2+( yP yQ )2 .
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.
(a) If AF=BF , can we conclude A=B ? (b) If AF=BF , can we conclude A=B ? (c) If FA=BF , can we conclude A=B ? Why or why not?
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.
A surveyor measures the distance across a river that flows straight north by the following method. Starting directly across from a tree on the opposite bank, the surveyor walks 100 m along the river to establish a baseline. She then sights across to the tree and reads that the angle from the baseline to the tree is 35 . How wide is the river?
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?