Book edition 7th

Author(s) Douglas C. Giancoli

Pages 978 pages

ISBN 978-0321625922

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Short Answer

A car is driven 225 km west and then 98 km southwest (45°). What is the displacement of the car from the point of origin (magnitude and direction)? Draw a diagram.

The magnitude of the displacement of the car from the point of origin is 302.3 km, and the direction is $13.2 °$ south of the west.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Meaning of displacement

The net displacement of an object can be defined as the vector addition of the object's individual displacement in various directions. If the object's initial and final points are similar, the object's net displacement value is zero.

Step 2. Given information

Given data:

The displacement of the car in the western direction is ${\vec{D}}_{w e s t} = 225 km$ .

The displacement of the car in the southwestern direction $(θ = 45 °)$ is ${\vec{D}}_{s o u t h - w e s t} = 98 km$ .

Step 3. Vector diagram

The vector diagram for the problem can be drawn as follows:

Step 4. Calculate the resultant displacement vector in the western direction

The resultant displacement vector in the western direction can be calculated as

$\begin{matrix} {\vec{D}}_{R - w e s t} = {\vec{D}}_{w e s t} + {\vec{D}}_{s o u t h - w e s t} \cos θ \\ {\vec{D}}_{R - w e s t} = (225 km) + (98 km) \cos (45 °) \\ {\vec{D}}_{R - w e s t} = 294.3 km \end{matrix}$

Step 5. Calculate the resultant displacement vector in the southwestern direction

The resultant displacement vector in the southwestern direction can be calculated as

$\begin{matrix} {\vec{D}}_{R - s o u t h w e s t} = {\vec{D}}_{s o u t h - w e s t} \sin θ \\ {\vec{D}}_{R - s o u t h w e s t} = (98 km) \sin (45 °) \\ {\vec{D}}_{R - s o u t h w e s t} = 69.3 km \end{matrix}$

Step 6. Calculate the magnitude of the resultant displacement vector

The magnitude of the resultant displacement vector can be calculated as

$\begin{matrix} {\vec{D}}_{R} = \sqrt{{({\vec{D}}_{R - w e s t})}^{2} + {({\vec{D}}_{R - s o u t h w e s t})}^{2}} \\ {\vec{D}}_{R} = \sqrt{{(294.3 km)}^{2} + {(69.3 km)}^{2}} \\ {\vec{D}}_{R} = 302.3 km \end{matrix}$

Step 7. Calculate the direction for the resultant displacement vector

The direction for the resultant displacement vector can be calculated as

$\begin{matrix} θ = \tan^{- 1} (\frac{{\vec{D}}_{R - s o u t h w e s t}}{{\vec{D}}_{R - w e s t}}) \\ θ = \tan^{- 1} (\frac{69.3 km}{294.3 km}) \\ θ = 13.2 ° \end{matrix}$

Thus, the magnitude of the displacement of the car from the point of origin is 302.3 km, and the direction is $13.2 °$ south of the west.

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Physics Principles with Applications

Answers without the blur.

Short Answer

A car is driven 225 km west and then 98 km southwest (45°). What is the displacement of the car from the point of origin (magnitude and direction)? Draw a diagram.

Step by Step Solution

Step 1. Meaning of displacement

Step 2. Given information

Step 3. Vector diagram

Step 4. Calculate the resultant displacement vector in the western direction

Step 5. Calculate the resultant displacement vector in the southwestern direction

Step 6. Calculate the magnitude of the resultant displacement vector

Step 7. Calculate the direction for the resultant displacement vector

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Select your language

Physics Principles with Applications

Answers without the blur.

Short Answer

A car is driven 225 km west and then 98 km southwest (45°). What is the displacement of the car from the point of origin (magnitude and direction)? Draw a diagram.

Step by Step Solution

Step 1. Meaning of displacement

Step 2. Given information

Step 3. Vector diagram

Step 4. Calculate the resultant displacement vector in the western direction

Step 5. Calculate the resultant displacement vector in the southwestern direction

Step 6. Calculate the magnitude of the resultant displacement vector

Step 7. Calculate the direction for the resultant displacement vector

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