Q3E Find the north and east componen... [FREE SOLUTION]

91影视

Chapter 3: Q3E (page 121)

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

Short Answer

Expert verified

The east component is 3.8 km

The north component is 3.2 km

Step by step solution

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.

Determine the displacement of the hiker towards the north component

In triangle ABC:

$\begin{array}{rcl} 鈭� A B C & = & 90^{掳} - 40^{掳} \\ = & 50^{掳} \end{array}$

$BC = 5 km$

AC = Base

BC = Hypotenuse

AB = Perpendicular

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

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

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:

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

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

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

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

Short Answer

Step by step solution

Vector definition

Determine the displacement of the hiker towards the north component

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Particle Model of Matter

Mechanics and Materials

Force

Engineering Physics

Radiation

Magnetism

Study anywhere. Anytime. Across all devices.