A vector has an x-component of -23.0 units and a y-component of 28.5 units. Find the magnitude and direction of the vector. magnitude units direction • (counterclockwise from the +x-axis)
A vector has an x-component of -23.0 units and a y-component of 28.5 units. Find the magnitude and direction of the vector. magnitude units direction • (counterclockwise from the +x-axis)
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![### Vector Magnitude and Direction Calculation
A vector has an x-component of **−23.0 units** and a y-component of **28.5 units**. Find the magnitude and direction of the vector.
- **Magnitude:** _______ units
- **Direction:** _______° (counterclockwise from the +x-axis)
To solve this problem, you can use the following formulas:
1. **Magnitude of the vector** is given by:
\[
\text{Magnitude} = \sqrt{(x^2 + y^2)}
\]
2. **Direction of the vector** (θ), measured counterclockwise from the positive x-axis, can be calculated using:
\[
\theta = \tan^{-1}\left(\frac{y}{x}\right)
\]
Note: When calculating the direction, consider the signs of x and y to determine the correct quadrant for θ.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d158991-3671-4459-aef6-bd0615668acc%2F1ed5eba7-888c-497f-aeba-e111a0a5611f%2Ftu7hq2d_processed.png&w=3840&q=75)
Transcribed Image Text:### Vector Magnitude and Direction Calculation
A vector has an x-component of **−23.0 units** and a y-component of **28.5 units**. Find the magnitude and direction of the vector.
- **Magnitude:** _______ units
- **Direction:** _______° (counterclockwise from the +x-axis)
To solve this problem, you can use the following formulas:
1. **Magnitude of the vector** is given by:
\[
\text{Magnitude} = \sqrt{(x^2 + y^2)}
\]
2. **Direction of the vector** (θ), measured counterclockwise from the positive x-axis, can be calculated using:
\[
\theta = \tan^{-1}\left(\frac{y}{x}\right)
\]
Note: When calculating the direction, consider the signs of x and y to determine the correct quadrant for θ.
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