Concept explainers
(a)
The magnitude and direction of the vector.
(a)
Answer to Problem 56P
The magnitude and direction of the vector is
Explanation of Solution
Write the expression to determine the magnitude of the vector.
Write the expression to determine the direction of the vector.
Calculate the components of each given vectors by substituting
Solve for
The magnitude of the vector from expression (I)
The direction of the vector from expression (II)
Conclusion:
The magnitude and direction of the vector is
(b)
The magnitude and direction of the vector.
(b)
Answer to Problem 56P
The magnitude and direction of the vector is
Explanation of Solution
Write the expression to determine the magnitude of the vector.
Write the expression to determine the direction of the vector.
Calculate the components of each given vectors by substituting
Solve for
The magnitude of the vector from expression (I)
The direction of the vector from expression (II)
Conclusion:
The magnitude and direction of the vector is
(c)
The magnitude and direction of the vector.
(c)
Answer to Problem 56P
The magnitude and direction of the vector is
Explanation of Solution
Write the expression to determine the magnitude of the vector.
Write the expression to determine the direction of the vector.
Calculate the components of each given vectors by substituting
Solve for
The magnitude of the vector from expression (I)
The direction of the vector from expression (II)
Conclusion:
The magnitude and direction of the vector is
(d)
The magnitude and direction of the vector.
(d)
Answer to Problem 56P
The magnitude and direction of the vector is
Explanation of Solution
Write the expression to determine the magnitude of the vector.
Write the expression to determine the direction of the vector.
Calculate the components of each given vectors by substituting
Solve for
The magnitude of the vector from expression (I)
The direction of the vector from expression (II)
Conclusion:
The magnitude and direction of the vector is
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Chapter 1 Solutions
College Physics, Volume 1
- At one point in space, the direction of the electric field vector Is given In the Cartesian system by the unit vector . If the magnitude of the electric field vector is E=400.0V/m , what are the scalar components , and of the electric field vector at this point? What is the direction angle of the electric field vector at this point?arrow_forwardFigure 1.19 shows two vectors lying in the xy-plane. Determine the signs of the x- and y-components of A, B, and A+B.arrow_forwardVector B has x, y, and z components of 4.00, 6.00, and 3.00 units, respectively. Calculate (a) the magnitude of B and (b) the angle that B makes with each coordinate axis.arrow_forward
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- A vector points from the origin into the second quadrant of the xy plane. What can you conclude about its components? (a) Both components are positive. (b) The x component is positive, and the y component is negative. (c) The x component is negative, and the y component is positive. (d) Both components are negative. (e) More than one answer is possible.arrow_forwardX is an unknown vector satisfying the following relations involving the known vectors A and B and the scalar ϕ, A × X = B, A · X = ϕ. Express X in terms of A, B, ϕ, and the magnitude of A.arrow_forwardTwo points in the Cartesian plane are A(2.00m,4.00m) and B(-3.00m,3.00m) . Find the distance between them and their polar coordinates.arrow_forward
- A pirate has buried his treasure on an island with five trees located at the points (30.0 m, 20.0 m), (60.0 m, 80.0 m), (10.0 m, 10.0 m), (40.0 m, 30.0 m), and (70.0 m, 60.0 m), all measured relative to some origin, as shown in Figure P1.69. His ships log instructs you to start at tree A and move toward tree B, but to cover only one-half the distance between A and B. Then move toward tree C, covering one-third the distance between your current location and C. Next move toward tree D, covering one-fourth the distance between where you are and D. Finally move toward tree E, covering one-fifth the distance between you and E, stop, and dig. (a) Assume you have correctly determined the order in which the pirate labeled the trees as A, B, C, D, and E as shown in the figure. What are the coordinates of the point where his treasure is buried? (b) What If? What if you do not really know the way the pirate labeled the trees? What would happen to the answer if you rearranged the order of the trees, for instance, to B (30 m, 20 m), A (60 m, 80 m), E (10 m, 10 m), C (40 m, 30 m), and D (70 m, 60 m)? State reasoning to show that the answer does not depend on the order in which the trees are labeled. Figure 1.69arrow_forwardConsider 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.arrow_forwardThree displacement vectors of a croquet ball are shown in Figure P1.44, where |A|=20.0units, |B|=40.0units, and |C|=30.0units. Find (a) the resultant in unit-vector notation and (b) the magnitude and direction of the resultant displacement. Figure P1.44arrow_forward
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