1. A velocity vector has components v₁ = -36 m/s and vy=22 m/s What is magnitude this velocity vector? A.. 58 m/s B 42 m/s C. 32 m/s D. 14 m/s F 7.2 m/s
1. A velocity vector has components v₁ = -36 m/s and vy=22 m/s What is magnitude this velocity vector? A.. 58 m/s B 42 m/s C. 32 m/s D. 14 m/s F 7.2 m/s
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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![**Physics Question: Calculating the Magnitude of a Velocity Vector**
**Problem Statement:**
A velocity vector has components \(v_x = -36 \, \text{m/s}\) and \(v_y = 22 \, \text{m/s}\). What is the magnitude of this velocity vector?
**Answer Choices:**
A. \(58 \, \text{m/s}\)
B. \(42 \, \text{m/s}\)
C. \(32 \, \text{m/s}\)
D. \(14 \, \text{m/s}\)
E. \(7.2 \, \text{m/s}\)
---
**Explanation:**
To determine the magnitude of the velocity vector, you can use the Pythagorean theorem, given that you have the velocity components in the x and y directions.
The formula to calculate the magnitude (v) of the velocity vector is:
\[
v = \sqrt{v_x^2 + v_y^2}
\]
Given:
- \(v_x = -36 \, \text{m/s}\)
- \(v_y = 22 \, \text{m/s}\)
Plugging in these values:
\[
v = \sqrt{(-36)^2 + 22^2}
\]
\[
v = \sqrt{1296 + 484}
\]
\[
v = \sqrt{1780}
\]
Approximating the square root:
\[
v \approx 42.2 \, \text{m/s}
\]
Thus, the correct answer is:
B. \(42 \, \text{m/s}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45088ba1-a1a3-4a96-b462-54f2c0a5a29e%2F6955eb35-4f45-4d30-bc15-cf3e08ed4c5e%2F8ifet2c_processed.png&w=3840&q=75)
Transcribed Image Text:**Physics Question: Calculating the Magnitude of a Velocity Vector**
**Problem Statement:**
A velocity vector has components \(v_x = -36 \, \text{m/s}\) and \(v_y = 22 \, \text{m/s}\). What is the magnitude of this velocity vector?
**Answer Choices:**
A. \(58 \, \text{m/s}\)
B. \(42 \, \text{m/s}\)
C. \(32 \, \text{m/s}\)
D. \(14 \, \text{m/s}\)
E. \(7.2 \, \text{m/s}\)
---
**Explanation:**
To determine the magnitude of the velocity vector, you can use the Pythagorean theorem, given that you have the velocity components in the x and y directions.
The formula to calculate the magnitude (v) of the velocity vector is:
\[
v = \sqrt{v_x^2 + v_y^2}
\]
Given:
- \(v_x = -36 \, \text{m/s}\)
- \(v_y = 22 \, \text{m/s}\)
Plugging in these values:
\[
v = \sqrt{(-36)^2 + 22^2}
\]
\[
v = \sqrt{1296 + 484}
\]
\[
v = \sqrt{1780}
\]
Approximating the square root:
\[
v \approx 42.2 \, \text{m/s}
\]
Thus, the correct answer is:
B. \(42 \, \text{m/s}\)
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