### Vector Addition Problem#### Given:- Distance \(a = 4.3 \, \text{m}\)- Distance \(b = 7.7 \, \text{m}\)- Magnitude of vector \(\mathbf{F}_1 = 28 \, \text{N}\)- Magnitude of vector \(\mathbf{F}_2 = 37.7 \, \text{N}\)#### Objective:Find the magnitude of the resultant vector \(\mathbf{F}_1 + \mathbf{F}_2\). Round your answer to one decimal place.#### Explanation:The accompanying diagram represents a vector problem in a coordinate system where:- \(\mathbf{F}_1\) is a force vector directed at an angle above the horizontal axis.- \(\mathbf{F}_2\) is a force vector directed horizontally to the left.The distances \(a\) and \(b\) are used to determine the direction of the forces:- Distance \(a\) is the horizontal component of vector \(\mathbf{F}_1\).- Distance \(b\) is the vertical component of vector \(\mathbf{F}_1\).The task is to determine the resultant vector by summing these two vectors and finding the magnitude of the resultant.#### Steps:1. **Determine the Components of Vectors:** - For \(\mathbf{F}_1\): Given the right triangle formed by \(a\) and \(b\), use trigonometric relations to find the components. \[ \text{angle} \theta = \tan^{-1} \left( \frac{b}{a} \right) = \tan^{-1} \left( \frac{7.7}{4.3} \right) \] Use this angle \(\theta\) to resolve \(\mathbf{F}_1\) into components: \[ F_{1x} = F_1 \cos(\theta) \quad \text{and} \quad F_{1y} = F_1 \sin(\theta) \]2. **Vector Addition:** \[ \mathbf{F}_{\text{total}} = \mathbf{F}_1 + \mathbf{F}_2 \] Find the total x and y components: \[ F_{\text{total},

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Answered: If a = 4.3 m and b = 7.7 m. Find the…

If a = 4.3 m and b = 7.7 m. Find the magnitude of Fi+F2 give the magnitude F1 =28 N and and F2=37.7 N. Round your answer to 1 decimal place.

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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Scalars and Vectors

Scalars and Vectors are the classification of physical quantities that are used to denote various terms in physics.

Question

### Vector Addition Problem

#### Given:
- Distance \(a = 4.3 \, \text{m}\)
- Distance \(b = 7.7 \, \text{m}\)
- Magnitude of vector \(\mathbf{F}_1 = 28 \, \text{N}\)
- Magnitude of vector \(\mathbf{F}_2 = 37.7 \, \text{N}\)

#### Objective:
Find the magnitude of the resultant vector \(\mathbf{F}_1 + \mathbf{F}_2\). Round your answer to one decimal place.

#### Explanation:
The accompanying diagram represents a vector problem in a coordinate system where:
- \(\mathbf{F}_1\) is a force vector directed at an angle above the horizontal axis.
- \(\mathbf{F}_2\) is a force vector directed horizontally to the left.

The distances \(a\) and \(b\) are used to determine the direction of the forces:
- Distance \(a\) is the horizontal component of vector \(\mathbf{F}_1\).
- Distance \(b\) is the vertical component of vector \(\mathbf{F}_1\).

The task is to determine the resultant vector by summing these two vectors and finding the magnitude of the resultant.

#### Steps:
1. **Determine the Components of Vectors:**
- For \(\mathbf{F}_1\): Given the right triangle formed by \(a\) and \(b\), use trigonometric relations to find the components.
\[
\text{angle} \theta = \tan^{-1} \left( \frac{b}{a} \right) = \tan^{-1} \left( \frac{7.7}{4.3} \right)
\]
Use this angle \(\theta\) to resolve \(\mathbf{F}_1\) into components:
\[
F_{1x} = F_1 \cos(\theta) \quad \text{and} \quad F_{1y} = F_1 \sin(\theta)
\]

2. **Vector Addition:**
\[
\mathbf{F}_{\text{total}} = \mathbf{F}_1 + \mathbf{F}_2
\]
Find the total x and y components:
\[
F_{\text{total},

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