COLLEGE PHYSICS
2nd Edition
ISBN: 9781464196393
Author: Freedman
Publisher: MAC HIGHER
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Chapter 3, Problem 27QAP
To determine
The vector components of
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Consider vectors A- 4.0 î + 3.0j and B- 4.0i + 8.0
Part A
Calculate A+ B. Express your answer as ri + yj
Enter the x and y components of the vector separated
by a comma.
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• Part B
Calculate A - B. Express your answer as + ui
Enter the x and y components of the vector separated
by a comma.
?
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• Part C
If the direction (but not the magnitude) of B is allowed
to change by any amount you like, how large can JA+
Bị be?
?
11
11
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If the direction (but not the magnitude) of B is allowed
to change by any amount you like, how small can |A +
Bj be?
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Vector A has a magnitude of 40 units and points in the positive y direction.
When vector i is added to Ā, the resultant vector à + 5 points in the negative
y direction with a magnitude of 13 units. Find the magnitude and direction of
в.
magnitude
unit(s)
• counterclockwise from the +x-axis
direction
R
70
140
The two vectors shown, R and S, each have a magnitude of 5 meters.
A) Calculate the magnitude of the difference of these vectors: R-S.
B) Calculate the angle R-S relative to the positive x axis.
C) Sketch the graphical vector subtraction R – S on the graph (sketch the x-y coordinates if needed)
to see the direction that R-S points. The drawn direction does not have to be very accurate, but
should point towards the right quadrant and be consistent with your answer in B).
I.
Chapter 3 Solutions
COLLEGE PHYSICS
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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_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_forwardThe displacement vectors 42.0 cm at 15.0 and 23.0 cm at 65.0 both start from the origin and form two sides of a parallelogram. Both angles are measured counterclockwise from the x axis. (a) Find the area of the parallelogram. (b) Find the length of its longer diagonal.arrow_forward
- Three 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_forwardAt 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_forwardLei B = 5.00 m at 60.0. Let the vector C have the same magnitude as A and a direction angle greater than that of A by 25.0. Let A B = 30.0 m2 and B C = 35.0 m2. Find the magnitude and direction of A.arrow_forward
- Figure 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 A has x and y components of 8.70 cm and 15.0 cm, respectively; vector B has x and y components of 13.2 cm and 6.60 cm, respectively. If AB+3C=0, what are the components of C?arrow_forwardThe resultant vector R=2AB2C has zero magnitude. Vector A has an x component of 4.60 m and a y component of 12.1 m. and vector B has an x component of 3.00 m and a y component of 4.00 m. What are the x and y components of vector C? (All of these are two-dimensional vectors.)arrow_forward
- Use the component method to add the vectors A and B shown in Figure P1.34. Express the resultant A+B in unit-vector notation. 34. The displacement vectors A and B shown in Figure P1.34 have magnitudes of 3.00 m. The direction of vector A is = 30.0. Find graphically (a) A+B, (b) AB, (c) BA, and (d) A2B. (Report all angles counterclockwise from the positive x axis.)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_forwardVector A has a magnitude of 4.50 m and makes an angle of 64.0 with the positive x axis. Vector B, with a magnitude equal to that of vector A, points along the negative y axis (Fig. P3.16). Graphically find the magnitude and direction of the resultant vector a. A+B, b. AB, c. BA, and d. 2AB.arrow_forward
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