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(a)
The components of the vector
Answer to Problem 32QAP
The x component of the vector
Explanation of Solution
Given:
The components of the vectors
Formula used:
If
And the y component of
Calculation:
Substitute the given values of the variables in the formula and calculate the x component.
Substitute the given values of the variables in the formula and calculate the y component.
Conclusion:
The x component of the vector
(b)
The components of the vector
Answer to Problem 32QAP
The x component of the vector
Explanation of Solution
Given:
The components of the vectors
Formula used:
If
The y component is given by,
Calculation:
Substitute the given values of the variables in the formula and calculate the x component.
Substitute the given values of the variables in the formula and calculate the y component.
Conclusion:
The x component of the vector
(c)
The components of the vector
Answer to Problem 32QAP
The x component of the vector
Explanation of Solution
Given:
The components of the vectors
Formula used:
If
The y component is given by,
Calculation:
Substitute the given values of the variables in the formula and calculate the x component.
Substitute the given values of the variables in the formula and calculate the y component.
Conclusion:
The x component of the vector
(d)
The components of the vector
Answer to Problem 32QAP
The x component of the vector
Explanation of Solution
Given:
The components of the vectors
Formula used:
If
The y component is given by,
Calculation:
Substitute the given values of the variables in the formula and calculate the x component of the vector
Substitute the given values of the variables in the formula and calculate the y component of the vector
Conclusion:
The x component of the vector
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Chapter 3 Solutions
COLLEGE PHYSICS,VOLUME 1
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- Suppose you walk 18.0 m straight west and then 25.0 m straight north. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements A and B as in Figure 3.55, then this problem asks you to find their sum R=A+B .)arrow_forwardA 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 P3.46. 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 P3.46arrow_forwardSuppose you first walk 12.0 m in a direction 20° west of north and then 20.0 m in a direction 40.0° south of west. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements A and B, as in Figure 3.56, then this problem finds their sum R=A+B. )arrow_forward
- A snow-covered ski slope makes an angle of 35.0 with the horizontal. When a ski jumper plummets onto the hill, a parcel of splashed snow is thrown up to a maximum displacement of 1.50 m at 16.0 from the vertical in the uphill direction as shown in Figure P3.16. Find the components of its maximum displacement (a) parallel to the surface and (b) perpendicular to the surface. Figure P3.16arrow_forwardGive a specific example of a vector, stating its magnitude, units, and direction.arrow_forwardUnder what conditions is the magnitude of the vector sum A~ + ~B equal to the sum of the magnitudes of the two vectors? Explain briefly.arrow_forward
- 1. Determine the equivalent directions for the given vectors. a. 35° N of E b. 20° W of S c. S 40° E d. N 65° W 2. Determine the equilibrant of the given vectors by (a) parallelogram method and (b) triangle method. Use the given scale for your answer. C = 10 kph, 12degrees N of W E = 15 kph, 83degrees S of E 3. A sailor in a small boat encounters shifting winds. She sails 8 km south, then 15 km 30o E of N, and then 12 km 25o N of W. Use polygon method to determine the magnitude and direction of her resultant displacement. 4. Solve for the required using the given vectors A = 3i – 8j + 6k B = 4 j + 9k – 5i C = 7k a. A ∙B b. A ×B c. (A ×B)×C d. (B×C)∙Aarrow_forwardA vector has zero magnitude. Is it necessary to specify its direction? Explain.arrow_forwardVector A has a magnitude of 3.2 m/s and vector B has a magnitude of 5.3 m/s. If you can change the directions of A and B (but not their magnitudes) what are the limits on the length of A + B ?arrow_forward
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