Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

The two vectors $\vec{a} a n d \vec{b}$ in Fig.3.28 have equal magnitudes of 10.0m and the angles are $θ = 30 °$ and $θ = 105 °$ . Find the (a) x and (b) y components of their vector sum $\vec{r}$ , (c) the magnitude of $\vec{r}$ , and (d) the angle $\vec{r}$ makes with the positive direction of the x axis

a) x component of vector sum $\vec{r} is 1.59 m$

b) y component of vector sum $\vec{r} is 12.1 m$

c) Magnitude of vector sum $\vec{r} is 12.2 m$

c) Angle $\vec{r} is 82.5 °$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: To understand the concept

This problem involves the addition of two vectors $\vec{a}$ and $\vec{b}$ . Using the following relations x and y components of the vector sum $\vec{r}$ can be found and similarly the magnitude and the angle respectively.

localid="1656155400549" $r = \vec{|r|} = \sqrt{{(x)}^{2} + {(y)}^{2}}$ (i)

$θ = \tan^{- 1} (\frac{y}{x})$ (ii)

Given

Two vectors and $\vec{a} = 10 m and \vec{b} = 10 m$

two angles and $θ_{1} = 30 ° and θ_{2} = 105 °$

Step 2: To find x component of vector sum r→

x component of the vector sum r is given by

$r_{x} = a \cos θ_{1} + b \cos θ_{2} \vec{r} = 10 m \times \cos (30) + 10 m \times (135) r_{x} = 1.59 m$

Step 3: To find y component of vector sum r→

y component of vector sum $\vec{r}$ is

$r_{y} = a {sinθ}_{1} + {bsinθ}_{2} \vec{r} = 10 m \times \sin (30) + 10 m \times \sin (135) r_{y} = 12.1 m$

Step 4: To find magnitude of vector sum r→

Using equation (i) the magnitude of vector $\vec{r}$ is written as

$r = \vec{|r|} = \sqrt{(1.59 m^{2}) + {(12.1 m)}^{2}} r = 12.2 m$

Step 5: To find angle of vector sum r→

The angle $\vec{r}$ makes with the positive direction of the x axis is

$\tan^{1} (\frac{12.1}{1.59}) = 82.5 °$

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Fundamentals Of Physics

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Short Answer

Step by Step Solution

Step 1: To understand the concept

Step 2: To find x component of vector sum r→

Step 3: To find y component of vector sum r→

Step 4: To find magnitude of vector sum r→

Step 5: To find angle of vector sum r→

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Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

The two vectors a →and b→ in Fig.3.28 have equal magnitudes of 10.0m and the angles are θ=30°and θ=105° . Find the (a) x and (b) y components of their vector sumr→ , (c) the magnitude of r→, and (d) the angler→makes with the positive direction of the x axis

Step by Step Solution

Step 1: To understand the concept

Step 2: To find x component of vector sum r→

Step 3: To find y component of vector sum r→

Step 4: To find magnitude of vector sum r→

Step 5: To find angle of vector sum r→

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