Skip to main content
Ch 01: Units, Physical Quantities & Vectors
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 14th EditionCh 01: Units, Physical Quantities & VectorsProblem 27
Chapter 1, Problem 27

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

Verified step by step guidance
1
Identify the vectors and their respective angles with the positive x-axis: Vector N (14 cm, 13°), Vector M (21 cm, 62°), Vector P (17 cm, 40°), and Vector O (25 cm, 45°).
For each vector, use the trigonometric functions to find the x-component: x-component = magnitude * cos(angle).
For each vector, use the trigonometric functions to find the y-component: y-component = magnitude * sin(angle).
Apply the formulas to Vector N: x-component = 14 * cos(13°), y-component = 14 * sin(13°).
Apply the formulas to Vector M: x-component = 21 * cos(62°), y-component = 21 * sin(62°).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
5m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Vector Components

Vectors can be broken down into their x- and y-components, which represent the vector's influence in the horizontal and vertical directions, respectively. This is done using trigonometric functions: the x-component is found using the cosine of the angle, and the y-component is found using the sine of the angle, both multiplied by the vector's magnitude.
Recommended video:
Guided course
07:30
Vector Addition By Components

Trigonometric Functions

Trigonometric functions, such as sine and cosine, are essential for resolving vectors into components. For a vector at an angle θ from the positive x-axis, the cosine function helps find the adjacent side (x-component), while the sine function helps find the opposite side (y-component) of the right triangle formed by the vector.
Recommended video:
Guided course
08:30
Intro to Wave Functions

Reference Angles and Quadrants

Understanding the quadrant in which a vector lies is crucial for determining the signs of its components. Angles are typically measured from the positive x-axis, and the sign of the components depends on the vector's direction: positive in the first quadrant, negative in the second for x, and so on. This helps in correctly applying trigonometric functions to find vector components.
Recommended video:
Guided course
14:10
Inertial Reference Frames
Related Practice
Textbook Question

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.

7
views
Textbook Question

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?

1
views
Textbook Question

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

1
views
Textbook Question

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.

20
views
1
rank
Textbook Question

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

6
views
Textbook Question

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


1
views