Skip to main content
Ch 01: Units, Physical Quantities & Vectors
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 15th EditionCh 01: Units, Physical Quantities & VectorsProblema 24a
Capitolo 1, Problema 24a

Let θ be the angle that the vector A makes with the +x-axis, measured counterclockwise from that axis. Find angle θ for a vector that has these components: Ax = 2.00m, Ay = −1.00 m

Guida verificata passo dopo passo
1
Start by understanding that the angle θ is the angle between the vector A and the positive x-axis. This angle can be found using trigonometric functions, specifically the tangent function, which relates the opposite side to the adjacent side in a right triangle.
The components of the vector A are given as Ax = 2.00 m and Ay = -1.00 m. These components represent the horizontal and vertical sides of the triangle formed by the vector.
Use the tangent function to find the angle θ. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Therefore, tan(θ) = Ay / Ax. Substitute the given values into this equation: tan(θ) = -1.00 m / 2.00 m.
To find the angle θ, take the arctangent (inverse tangent) of the ratio calculated in the previous step. This will give you θ = arctan(-1.00 m / 2.00 m).
Since the tangent function can have multiple solutions, consider the direction of the vector components. The negative Ay indicates that the vector is pointing downward, so the angle θ will be in the fourth quadrant. Adjust the angle accordingly to ensure it is measured counterclockwise from the positive x-axis.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Concetti chiave

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

Vector Components

Vector components are the projections of a vector along the axes of a coordinate system. In this problem, Ax and Ay represent the horizontal and vertical components of vector A, respectively. Understanding these components is crucial for determining the direction and magnitude of the vector.
Video consigliato:
Percorso guidato
07:30
Vector Addition By Components

Trigonometric Functions

Trigonometric functions, such as tangent, sine, and cosine, relate the angles and sides of a right triangle. To find the angle θ that a vector makes with the x-axis, the tangent function is used, defined as the ratio of the opposite side (Ay) to the adjacent side (Ax). This relationship helps calculate the angle from the vector components.
Video consigliato:
Percorso guidato
08:30
Intro to Wave Functions

Inverse Trigonometric Functions

Inverse trigonometric functions, like arctan, are used to find angles from known ratios of sides. In this context, arctan(Ay/Ax) will yield the angle θ that the vector makes with the +x-axis. This function is essential for converting the component ratio into an angle measurement.
Video consigliato:
Percorso guidato
08:30
Intro to Wave Functions
Pratica correlata
Domanda del libro di testo

For the vectors A and B in Fig. E1.24, use a scale drawing to find the magnitude and direction of the vector difference A − B.

2411
views
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?

2434
views
Domanda del libro di testo

Compute the x- and y-components of the vectors A, B, C, and D in Fig. E1.24.

4160
views
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.

4472
views
1
rank
1
comments
Domanda del libro di testo

A spelunker is surveying a cave. She follows a passage 180 m straight west, then 210 m in a direction 45° east of south, and then 280 m at 30° east of north. After a fourth displacement, she finds herself back where she started. Use a scale drawing to determine the magnitude and direction of the fourth displacement.

5495
views
2
rank
1
comments
Domanda del libro di testo

For the vectors A and B in Fig. E1.24, use a scale drawing to find the magnitude and direction of the vector sum A + B

6185
views