Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

Find the north and east components of the displacement for the hikers shown in Figure.

The east component is 3.8 km

The north component is 3.2 km

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Vector definition

A vector is a quantity that has both magnitude and direction. Displacement, velocity, force, torque, and other vector quantities are some examples of vector quantities.

Step 2: Determine the displacement of the hiker towards the north component

In triangle ABC:

$\begin{array}{rcl} ∠ A B C & = & 90^{°} - 40^{°} \\ = & 50^{°} \end{array}$

$BC = 5 km$

AC = Base

BC = Hypotenuse

AB = Perpendicular

For the north component, in the right-angled triangle:

$\begin{array}{rcl} \cos θ & = & \frac{b a s e}{h y p o t e n o u s} \\ \cos 50^{°} & = & \frac{b a s e}{5} \\ 0.64 & = & \frac{b a s e}{5} \\ b a s e & = & 3.2 k m \end{array}$

Therefore, towards the north component, the displacement of the hiker is 3.2 km.

Step 3: Determine the displacement of the hiker towards the east component

For the east component, in a right-angled triangle:

$\begin{array}{rcl} \sin θ & = & \frac{P e r p e n d i c u l a r}{h y p o t e n o u s} \\ \sin 50^{°} & = & \frac{p e r p e n d i c u l a r}{5} \\ 0.77 & = & \frac{p e r p e n d i c u l a r}{5} \\ P e r p e n d i c u l a r & = & 0.77 \times 5 \\ p e r p e n d i c u l a r & = & 3.8 k m \end{array}$

Therefore, towards the east component, the displacement of the hiker is 3.8 km.

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College Physics (Urone)

Answers without the blur.

Short Answer

Find the north and east components of the displacement for the hikers shown in Figure.

Step by Step Solution

Step 1: Vector definition

Step 2: Determine the displacement of the hiker towards the north component

Step 3: Determine the displacement of the hiker towards the east component

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College Physics (Urone)

Answers without the blur.

Short Answer

Find the north and east components of the displacement for the hikers shown in Figure.

Step by Step Solution

Step 1: Vector definition

Step 2: Determine the displacement of the hiker towards the north component

Step 3: Determine the displacement of the hiker towards the east component

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