Skip to main content
Ch 03: Vectors and Coordinate Systems
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 03: Vectors and Coordinate SystemsProblema 26
Capitolo 3, Problema 26

FIGURE P3.26 shows vectors A and B. Find D = 2A ＋B Write your answer in component form.

Guida verificata passo dopo passo
1
Step 1: Analyze the given vectors A and B in the diagram. Vector A has a magnitude of 5 m and is directed at an angle of 20° above the negative x-axis. Vector B has a magnitude of 3 m and is directed at an angle of 20° below the negative x-axis.
Step 2: Break down each vector into its components. For vector A, calculate the x-component as \( A_x = -A \cos(20°) \) and the y-component as \( A_y = A \sin(20°) \). Similarly, for vector B, calculate the x-component as \( B_x = -B \cos(20°) \) and the y-component as \( B_y = -B \sin(20°) \).
Step 3: Multiply vector A by 2 to account for the scalar multiplication in \( D = 2A + B \). The new components of 2A will be \( (2A_x, 2A_y) \).
Step 4: Add the components of 2A and B to find the components of vector D. Use \( D_x = 2A_x + B_x \) for the x-component and \( D_y = 2A_y + B_y \) for the y-component.
Step 5: Write the final result for vector D in component form as \( D = (D_x, D_y) \).

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
6m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Vector Addition

Vector addition involves combining two or more vectors to determine a resultant vector. This is done by adding the corresponding components of the vectors. In this case, the vectors A and B must be expressed in their component forms (x and y) before performing the addition to find the resultant vector D.
Video consigliato:
Percorso guidato
07:30
Vector Addition By Components

Component Form of Vectors

The component form of a vector expresses it in terms of its horizontal (x) and vertical (y) components. For a vector with magnitude and angle, the components can be calculated using trigonometric functions: Ax = A * cos(θ) and Ay = A * sin(θ). This allows for easier manipulation and addition of vectors.
Video consigliato:
Percorso guidato
07:30
Vector Addition By Components

Trigonometric Functions

Trigonometric functions, such as sine and cosine, relate the angles of a triangle to the ratios of its sides. In vector analysis, these functions are used to resolve vectors into their components. For example, the angle given in the problem (20 degrees) will be used to calculate the x and y components of vectors A and B, which are essential for finding the resultant vector D.
Video consigliato:
Percorso guidato
08:30
Intro to Wave Functions
Pratica correlata
Domanda del libro di testo

Find a vector that points in the same direction as the vector ( î ＋ ĵ ) and whose magnitude is 1.

3475
views
Domanda del libro di testo

What is the angle Φ between vectors E and F in FIGURE P3.24?

1893
views
Domanda del libro di testo

Use geometry and trigonometry to determine the magnitude and direction of G = E＋F.

1808
views
Domanda del libro di testo

The minute hand on a watch is 2.0 cm in length. What is the displacement vector of the tip of the minute hand in each case? Use a coordinate system in which the y-axis points toward the 12 on the watch face. From 8:00 to 8:20 a.m.

1765
views
Domanda del libro di testo

The minute hand on a watch is 2.0 cm in length. What is the displacement vector of the tip of the minute hand in each case? Use a coordinate system in which the y-axis points toward the 12 on the watch face. From 8:00 to 9:00 a.m.

1093
views
Domanda del libro di testo

Use components to determine the magnitude and direction of G = E＋F.

1634
views