Book edition 7th

Author(s) Douglas C. Giancoli

Pages 978 pages

ISBN 978-0321625922

Answers without the blur.

Just sign up for free and you're in.

Short Answer

Determine the vector $\vec{A} - \vec{C}$ with given the vectors $\vec{A}$ and $\vec{C}$
in Fig. 3–35.
FIGURE 3-35

The magnitude of the vector $\vec{A} - \vec{C}$ is $64.636$ , and the direction of this vector is $53.054 °$ from the positive x-axis in the anticlockwise direction.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Significance of a vector

A vector can be used to define the magnitude along with the direction of a physical quantity.

The resultant of two or more vectors can be calculated with the help of the addition or the subtraction of the horizontal and vertical components of the individual vectors.

Step 2. Determination of components of vector A→

The component of vector A in the x-direction can be calculated with the help of figure 3-35 given in the question as

$\begin{matrix} A_{x} = 44 \cos 28 ° \\ = 38.85 \end{matrix}$

The component of vector A in the y-direction can be expressed as

$\begin{matrix} A_{y} = 44 \sin 28 ° \\ = 20.657 \end{matrix}$

Step 3. Determination of components of vector C→

The inclination of the vector C from the x-axis in figure 3-35 can be given as

$\begin{matrix} ϕ = 90 ° + 90 ° + 90 ° \\ = 270 ° \end{matrix}$

Here, $ϕ$ is the angle of inclination of vector C with the positive x-axis in the clockwise direction.

The component of vector C in the x-direction can be calculated with the help of figure 3-35 given in the question as

$\begin{matrix} C_{x} = 31 \cos ϕ \\ = 31 \cos 270 ° \\ = 0 \end{matrix}$

The component of vector C in the –y-direction can be expressed as

$\begin{matrix} C_{y} = 31 \sin ϕ \\ = 31 \sin 270 ° \\ = - 31 \end{matrix}$

Step 4. Determination of the magnitude of A→-C→x

The magnitude of the component of vector $(\vec{A} - \vec{C})$ in the x-direction can be expressed as

$\begin{matrix} |{(\vec{A} - \vec{C})}_{x}| = A_{x} - C_{x} \\ = 38.85 - 0 \\ = 38.85 \end{matrix}$

Step 5. Determination of the magnitude of A→-C→y

The component of vector $(\vec{A} - \vec{C})$ in the y-direction can be expressed as

$\begin{matrix} |{(\vec{A} - \vec{C})}_{y}| = A_{y} - C_{y} \\ = 20.657 - (- 31) \\ = 51.657 \end{matrix}$

Step 6. Determination of the magnitude of the vector A→-C→

The magnitude of the vector can be calculated as

$|\vec{A} - \vec{C}| = \sqrt{{(|{(\vec{A} - \vec{C})}_{x}|)}^{2} + {(|{(\vec{A} - \vec{C})}_{y}|)}^{2}}$ .

Substituting the values in the above equation,

$\begin{matrix} |\vec{A} - \vec{C}| = \sqrt{{(38.85)}^{2} + {(51.657)}^{2}} \\ = 64.636 \end{matrix}$ .

Thus, the magnitude of the vector $\vec{A} - \vec{C}$ is $64.636$ .

Step 7. Determination of the direction of the vectorA→-C→

The direction of the vector can be expressed as

$\begin{matrix} \tan θ = \frac{A_{y} - C_{y}}{A_{x} - C_{x}} \\ θ = \tan^{- 1} \{\frac{A_{y} - C_{y}}{A_{x} - C_{x}}\} \end{matrix}$

Substituting the values in the above expression,

$\begin{matrix} θ = \tan^{- 1} (\frac{51.657}{38.85}) \\ = 53.054 ° \end{matrix}$

Thus, the direction of the vector $\vec{A} - \vec{C}$ is $53.054 °$ from the positive x-axis in the anticlockwise direction.

Find Study Materials for

Create Study Materials

Select your language

Physics Principles with Applications

Answers without the blur.

Short Answer

Determine the vector $\vec{A} - \vec{C}$ with given the vectors $\vec{A}$ and $\vec{C}$
in Fig. 3–35.
FIGURE 3-35

Step by Step Solution

Step 1. Significance of a vector

Step 2. Determination of components of vector A→

Step 3. Determination of components of vector C→

Step 4. Determination of the magnitude of A→-C→x

Step 5. Determination of the magnitude of A→-C→y

Step 6. Determination of the magnitude of the vector A→-C→

Step 7. Determination of the direction of the vectorA→-C→

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Physics Principles with Applications

Answers without the blur.

Short Answer

Determine the vector A→-C→ with given the vectors A→ and C→in Fig. 3–35.FIGURE 3-35

Step by Step Solution

Step 1. Significance of a vector

Step 2. Determination of components of vector A→

Step 3. Determination of components of vector C→

Step 4. Determination of the magnitude of A→-C→x

Step 5. Determination of the magnitude of A→-C→y

Step 6. Determination of the magnitude of the vector A→-C→

Step 7. Determination of the direction of the vectorA→-C→

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Famous Physicists

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics

Determine the vector $\vec{A} - \vec{C}$ with given the vectors $\vec{A}$ and $\vec{C}$
in Fig. 3–35.
FIGURE 3-35