Book edition 9th Edition

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

Pages 1624 pages

ISBN 9781133947271

Answers without the blur.

Just sign up for free and you're in.

Short Answer

Your dog is running around the grass in your back yard. He undergoes successive displacements $3.50 m$ south, 8.20 m northeast, and 15.0 m west. What is the resultant displacement?

$| \vec{R} | = 9.48 m, θ = 166 °$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Define magnitude and direction

In simple terms, magnitude means 'distance or number.' It depicts the absolute or relative size or direction in which an object moves in the feeling of motion. It's a term for describing the size or scope of something.
When we talk about direction, we're talking about a straight-line segment that connects two places in space. The direction is from the beginning (first) to the end (second).

Step 2: Determine the resultant displacement vector

Let us consider the given data.

$\vec{d_{1}} = - 3.5 m \hat{j} \vec{d_{2}} = (8.2 \times c o s 45 ° m) \hat{i} + (8.2 \times s i n 45 ° m) \hat{j} = (5.8 \hat{i} + 5.8 \hat{j}) m \vec{d_{3}} = - 15 m \hat{i}$

We sum the different displacements given in the problem to determine the resultant displacement.

$\vec{R} = \vec{d_{1}} + \vec{d_{2}} + \vec{d_{3}} = (- 15 + 5.8) m \hat{i} + (5.8 - 3.5) m \hat{j} = (- 9.2) m \hat{i} + (2.3) m \hat{j}$

Step 3: Determine the magnitude and direction of the resultant vector

The magnitude and direction of the resultant vector are then determined.

$| \vec{R} | = \sqrt{R_{x}^{2} + R_{y}^{2}} | \vec{R} | = \sqrt{{(- 9.2)}^{2} + {(2.3)}^{2}} | \vec{R} | = 9.48 m θ = \tan^{- 1} (\frac{R_{y}}{R_{x}}) + 180 ° = \tan^{- 1} (\frac{2.3}{- 9.2}) + 180 ° = 166 °$

Hence, the resultant displacement is $| \vec{R} | = 9.48 m, θ = 166 °$

Find Study Materials for

Create Study Materials

Select your language

Physics For Scientists & Engineers

Answers without the blur.

Short Answer

Your dog is running around the grass in your back yard. He undergoes successive displacements $3.50 m$ south, 8.20 m northeast, and 15.0 m west. What is the resultant displacement?

Step by Step Solution

Step 1: Define magnitude and direction

Step 2: Determine the resultant displacement vector

Step 3: Determine the magnitude and direction of the resultant vector

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Physics For Scientists & Engineers

Answers without the blur.

Short Answer

Your dog is running around the grass in your back yard. He undergoes successive displacements 3.50m south, 8.20 m northeast, and 15.0 m west. What is the resultant displacement?

Step by Step Solution

Step 1: Define magnitude and direction

Step 2: Determine the resultant displacement vector

Step 3: Determine the magnitude and direction of the resultant vector

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

Your dog is running around the grass in your back yard. He undergoes successive displacements $3.50 m$ south, 8.20 m northeast, and 15.0 m west. What is the resultant displacement?