Domanda del libro di testo
Vector A has y-component Ay = +9.60 m. A makes an angle of 32.0° counterclockwise from the +y-axis. (a) What is the x-component of A? (b) What is the magnitude of A?
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Ch 01: Units, Physical Quantities & Vectors
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552
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TOC.tableOfContents
- Ch 01: Units, Physical Quantities & Vectors37
- Ch 02: Motion Along a Straight Line57
- Ch 03: Motion in Two or Three Dimensions45
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws54
- Ch 06: Work & Kinetic Energy11
- Ch 07: Potential Energy & Conservation6
- Ch 08: Momentum, Impulse, and Collisions15
- Ch 09: Rotation of Rigid Bodies37
- Ch 10: Dynamics of Rotational Motion44
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics27
- Ch 13: Gravitation34
- Ch 14: Periodic Motion26
- Ch 15: Mechanical Waves22
- Ch 16: Sound & Hearing28
- Ch 17: Temperature and Heat28
- Ch 18: Thermal Properties of Matter35
- Ch 19: The First Law of Thermodynamics29
- Ch 20: The Second Law of Thermodynamics18
- Ch 21: Electric Charge and Electric Field28
- Ch 22: Gauss' Law21
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF24
- Ch 26: Direct-Current Circuits29
- Ch 27: Magnetic Field and Magnetic Forces16
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction22
- Ch 30: Inductance14
- Ch 31: Alternating Current20
- Ch 33: The Nature and Propagation of Light17
- Ch 34: Geometric Optics29
- Ch 35: Interference13
- Ch 36: Diffraction19
- Ch 37: Special Relativity19
- Ch 38: Photons: Light Waves Behaving as Particles12
- Ch 39: Particles Behaving as Waves25
- Ch 40: Quantum Mechanics I: Wave Functions20
- Ch 41: Quantum Mechanics II: Atomic Structure21
- Ch 42: Molecules and Condensed Matter17
- Ch 43: Nuclear Physics13
- Ch 44: Particle Physics and Cosmology17
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Non è quello che usi tu?Cambia libro di testo
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Young & Freedman Calc 15th EditionCh 01: Units, Physical Quantities & VectorsProblema 29a
Young & Freedman Calc 15th EditionCh 01: Units, Physical Quantities & VectorsProblema 29aCapitolo 1, Problema 29a
For the vectors A and B in Fig. E1.24 use the method of components to find the magnitude and direction of the vector sum A + B
Guida verificata passo dopo passo1
Identify the components of vector A. Since vector A is along the negative y-axis, its components are: \( A_x = 0 \) and \( A_y = -8.0 \text{ m} \).
Determine the components of vector B. Vector B makes a 30° angle with the positive y-axis. The components are: \( B_x = 15.0 \text{ m} \times \sin(30°) \) and \( B_y = 15.0 \text{ m} \times \cos(30°) \).
Calculate the x and y components of vector B using trigonometric functions: \( B_x = 15.0 \text{ m} \times 0.5 \) and \( B_y = 15.0 \text{ m} \times \sqrt{3}/2 \).
Add the components of vectors A and B to find the components of the resultant vector \( \vec{R} = \vec{A} + \vec{B} \). Thus, \( R_x = A_x + B_x \) and \( R_y = A_y + B_y \).
Calculate the magnitude of the resultant vector \( \vec{R} \) using the Pythagorean theorem: \( R = \sqrt{R_x^2 + R_y^2} \). Determine the direction by finding the angle \( \theta \) with respect to the x-axis using \( \theta = \tan^{-1}(R_y/R_x) \).
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Vector Addition
Vector addition involves combining two or more vectors to determine a resultant vector. This can be done graphically or analytically. In the graphical method, vectors are placed head-to-tail, while in the analytical method, the components of each vector are summed separately in the x and y directions to find the resultant's magnitude and direction.
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Percorso guidato
07:30
Vector Addition By Components
Components of a Vector
A vector can be broken down into its components along the x and y axes. The x-component is found using the cosine of the angle, while the y-component is determined using the sine of the angle. This decomposition simplifies calculations, allowing for the use of basic algebra to find the resultant vector's magnitude and direction.
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Percorso guidato
07:30Vector Addition By Components
Magnitude and Direction
The magnitude of a vector is its length, representing the quantity it describes, while the direction indicates where the vector points. The magnitude can be calculated using the Pythagorean theorem when the components are known, and the direction can be found using the arctangent function to determine the angle relative to a reference axis.
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Percorso guidato
03:59Calculating Magnitude & Components of a Vector
Pratica correlata
Domanda del libro di testo
Compute the x- and y-components of the vectors A, B, C, and D in Fig. E1.24.
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Domanda del libro di testo
A postal employee drives a delivery truck over the route shown in Fig. E1.25. Use the method of components to determine the magnitude and direction of her resultant displacement. In a vector-addition diagram (roughly to scale), show that the resultant displacement found from your diagram is in qualitative agreement with the result you obtained by using the method of components.
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Domanda del libro di testo
For the vectors A and B in Fig. E1.24 use the method of components to find the magnitude and direction of the vector difference B - A
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Domanda del libro di testo
Find the magnitude and direction of the vector represented by the following pairs of components: Ax = −8.60 cm, Ay = 5.20 cm
3433
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Domanda del libro di testo
For the vectors A and B in Fig. E1.24 use the method of components to find the magnitude and direction of the vector difference A - B
3883
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