Book edition 9th Edition

Author(s) Raymond A. Serway, John W. Jewett

Pages 1624 pages

ISBN 9781133947271

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Short Answer

Use the component method to add the $\vec{A}$ vectors and $\vec{B}$ shown in Figure P3.11. Both vectors have magnitudes of $3.00 m$ and vector $\vec{A}$ makes an angle of with the x axis. Express the resultant $\vec{A} + \vec{B}$ in unit-vector notation.

$\vec{A} + \vec{B} = (2 . 6 \hat{i} + 4 . 5 \hat{j}) m$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Define the components

In a two-dimensional coordinate system, the x-component and y-component are commonly considered to be the components of a vector. It can be written as_{$V = (v x, v y)$}with V denoting the vector.

These are the components of vectors created along the axes. In this article, we shall find the components of any given vector using formulas for both two-dimensional and three-dimensional coordinate systems.

$v_{x} = V \cos θ v_{y} = V \sin θ$

Step 2: State the given data

$A = 3 m B = 3 m θ_{A} = 30 ° θ_{B} = 90 °$

Step 3: Find the component vector A

Discover the following components to express A in component form:

$A_{x} = A \cos θ_{A} = 3 \cos (30 °) = 2.6 m$

$A_{y} = A \cos θ_{A} = 3 \cos (30 °) = 1.5 m$

$\vec{A} = A_{x} \hat{i} + A_{y} \hat{j} = (2 . 6 \hat{i} + 1 . 5 \hat{j}) m$

Step 4: Find the component vector B

Discover the following components to express B in component form

$B_{x} = 0 m B_{y} = 3 m \vec{B} = B_{x} \hat{i} + B_{y} \hat{j} = (3 \hat{j}) m$

Now find the resultant of A and B. We will add the components.

_{$\vec{A} + \vec{B} = (2 . 6 \hat{i} + 1 . 5 \hat{j}) m + (3 \hat{j}) m = (2 . 6 \hat{i} + 4 . 5 \hat{j}) m$}

The resultant vector is $\vec{A} + \vec{B} = (2 . 6 \hat{i} + 4 . 5 \hat{j}) m$

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Physics For Scientists & Engineers

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Short Answer

Use the component method to add the $\vec{A}$ vectors and $\vec{B}$ shown in Figure P3.11. Both vectors have magnitudes of $3.00 m$ and vector $\vec{A}$ makes an angle of with the x axis. Express the resultant $\vec{A} + \vec{B}$ in unit-vector notation.

Step by Step Solution

Step 1: Define the components

Step 2: State the given data

Step 3: Find the component vector A

Step 4: Find the component vector B

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Physics For Scientists & Engineers

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Short Answer

Use the component method to add the A→ vectors and B→ shown in Figure P3.11. Both vectors have magnitudes of 3.00m and vector A→ makes an angle of with the x axis. Express the resultant A→+B→ in unit-vector notation.

Step by Step Solution

Step 1: Define the components

Step 2: State the given data

Step 3: Find the component vector A

Step 4: Find the component vector B

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Use the component method to add the $\vec{A}$ vectors and $\vec{B}$ shown in Figure P3.11. Both vectors have magnitudes of $3.00 m$ and vector $\vec{A}$ makes an angle of with the x axis. Express the resultant $\vec{A} + \vec{B}$ in unit-vector notation.