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Given two vectors A = 4i + 7j and B = 5i - 2j, find the magnitude of each vector.
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Ch 01: Units, Physical Quantities & Vectors
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610
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TOC.tableOfContents
- Ch 01: Units, Physical Quantities & Vectors41
- Ch 02: Motion Along a Straight Line67
- Ch 03: Motion in Two or Three Dimensions47
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws59
- Ch 06: Work & Kinetic Energy14
- Ch 07: Potential Energy & Conservation8
- Ch 08: Momentum, Impulse, and Collisions18
- Ch 09: Rotation of Rigid Bodies42
- Ch 10: Dynamics of Rotational Motion48
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics31
- Ch 13: Gravitation35
- Ch 14: Periodic Motion32
- Ch 15: Mechanical Waves25
- Ch 16: Sound & Hearing32
- Ch 17: Temperature and Heat36
- Ch 18: Thermal Properties of Matter38
- Ch 19: The First Law of Thermodynamics33
- Ch 20: The Second Law of Thermodynamics22
- Ch 21: Electric Charge and Electric Field36
- Ch 22: Gauss' Law24
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF26
- Ch 26: Direct-Current Circuits30
- Ch 27: Magnetic Field and Magnetic Forces18
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction28
- Ch 30: Inductance17
- Ch 31: Alternating Current21
- Ch 32: Electromagnetic Waves1
- Ch 33: The Nature and Propagation of Light20
- Ch 34: Geometric Optics34
- Ch 35: Interference19
- Ch 36: Diffraction25
- Ch 37: Special Relativity20
- Ch 38: Photons: Light Waves Behaving as Particles15
- Ch 39: Particles Behaving as Waves26
- Ch 40: Quantum Mechanics I: Wave Functions21
- Ch 41: Quantum Mechanics II: Atomic Structure25
- Ch 42: Molecules and Condensed Matter18
- Ch 43: Nuclear Physics16
- Ch 44: Particle Physics and Cosmology23
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo
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Young & Freedman Calc 14th EditionCh 01: Units, Physical Quantities & VectorsProblema 34a
Young & Freedman Calc 14th EditionCh 01: Units, Physical Quantities & VectorsProblema 34aCapitolo 1, Problema 34a
Find the magnitude and direction of the vector represented by the following pairs of components: Ax = −8.60 cm, Ay = 5.20 cm
Guida verificata passo dopo passo1
Step 1: Understand that the vector components Ax and Ay represent the horizontal and vertical components of the vector, respectively. The magnitude of the vector can be found using the Pythagorean theorem.
Step 2: Use the formula for the magnitude of a vector: , where A and B are the components Ax and Ay. Substitute Ax = -8.60 cm and Ay = 5.20 cm into the formula.
Step 3: Calculate the magnitude of the vector using the formula: cm.
Step 4: Determine the direction of the vector using the tangent function. The direction angle θ can be found using the formula: . Substitute Ax = -8.60 cm and Ay = 5.20 cm into the formula.
Step 5: Calculate the direction angle θ using the formula: . Consider the signs of Ax and Ay to determine the correct quadrant for the angle.
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Vector Magnitude
The magnitude of a vector is a measure of its length and is calculated using the Pythagorean theorem. For a vector with components Ax and Ay, the magnitude is given by the formula √(Ax² + Ay²). This provides a scalar quantity representing the size of the vector irrespective of its direction.
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Calculating Magnitude & Components of a Vector
Vector Direction
The direction of a vector is determined by the angle it makes with a reference axis, typically the positive x-axis. This angle, θ, can be found using trigonometry, specifically the tangent function: θ = arctan(Ay/Ax). The angle provides insight into the vector's orientation in a coordinate system.
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06:44Adding 3 Vectors in Unit Vector Notation
Coordinate System
Understanding the coordinate system is crucial for interpreting vector components. In a Cartesian coordinate system, vectors are expressed in terms of their horizontal (x-axis) and vertical (y-axis) components. This system allows for the decomposition and analysis of vectors in two dimensions, facilitating calculations of magnitude and direction.
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Domanda del libro di testo
In each case, find the x- and y- components of vector A: A = 11.2j - 9.91i
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Domanda del libro di testo
Vector A is 2.80 cm long and is 60.0° above the x-axis in the first quadrant. Vector B is 1.90 cm long and is 60.0° below the x-axis in the fourth quadrant (Fig. E1.35). Use components to find the magnitude and direction of A - B In each case, sketch the vector addition or subtraction and show that your numerical answers are in qualitative agreement with your sketch.
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A disoriented physics professor drives 3.25 km north, then 2.20 km west, and then 1.50 km south. Find the magnitude and direction of the resultant displacement, using the method of components. 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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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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