/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q 62. Ian is planning a trip into the ... [FREE SOLUTION] | 91影视

91影视

Find study content
Learning Materials

Discover learning materials by subject, university or textbook.

Explanations

Textbooks
All Subjects

Anthropology

Archaeology

Architecture

Art and Design

Bengali

Biology

Business Studies

Greek

Chemistry

Chinese

Combined Science

Computer Science

Economics

Engineering

English

English Literature

Environmental Science

French

Geography

German

History

Hospitality and Tourism

Human Geography

Italian

Japanese

Law

Macroeconomics

Marketing

Math

Media Studies

Medicine

Microeconomics

Music

Nursing

Nutrition and Food Science

Physics

Polish

Politics

Psychology

Religious Studies

Sociology

Spanish

Sports Sciences

Translation

All Subjects

Biology

Business Studies

Chemistry

Combined Science

Computer Science

Economics

English

Environmental Science

Geography

History

Math

Physics

Psychology

Sociology
Features
Features

Discover all of these amazing features with a free account.

Flashcards

91影视 AI

Notes

Study Plans

Study Sets
What鈥檚 new?

Flashcards
Study your flashcards with three learning modes.

Study Sets
All of your learning materials stored in one place.

Notes
Create and edit notes or documents.

Study Plans
Organise your studies and prepare for exams.
91影视
Discover

All the hacks around your studies and career - in one place.

Find a degree

Magazine
Featured

Magazine
Trusted advice for anyone who wants to ace their studies & career.

The largest student job board with the most exciting opportunities.

Verified student deals from top brands.

Discover our mobile app to take your studies anywhere.

Learning Materials

Features

Discover

Chapter 14: Q 62. (page 1108)

Ian is planning a trip into the Wind River Range of mountains in Wyoming. He will carry ice gear, rock gear, and backpacking gear to a total of $80$ pounds. He will
follow a trail so that his position is given by
$(0.7 t^{2} + 1, 1.5 t (2 - t), 0.1 t^{3}) for t 鈭� [0, 1]$

Short Answer

Expert verified

The work done is $W = 80 {鈭�}_{0}^{1} \sqrt{10.96 t^{2} + 9 - 18 t + 0.09 t^{4}} d t$ .

Step by step solution

01

Given Information

It is given that position of trail is

$r (t) = <0.7 t^{2} + 1, 1.5 t (2 - t), 0.1 t^{3}>$

$t 鈭� [0, 1]$

02

Formula for calculating the work

As force is constant, work done is

$W = {鈭�}_{a}^{b} F 路 d r$

$= F {鈭�}_{a}^{b} d r$

$a, b$ are initial and final points.

Simplifying above with parametric coordinates

${鈭�}_{a}^{b} d r = {鈭�}_{t_{1}}^{t_{2}} ||r^{'} (t)|| d t$

parameter $t$ varies from $t_{1}$ to $t_{2}$

The integral for the trail is

${鈭�}_{t_{1}}^{t_{2}} ||r^{'} (t)|| d t = {鈭�}_{0}^{1} ||r^{'} (t)|| d t$

Hence, formula is

$W = 80 {鈭�}_{0}^{1} ||r^{'} (t)|| d t$

03

Calculation of Work

$r' (t)$ is calculated as

$r (t) = <0.7 t^{2} + 1, 1.5 t (2 - t), 0.1 t^{3}>$

$r^{'} (t) = <1.4 t, 3 (1 - t), 0.3 t^{2}>$

Norm of $r^{'} (t)$ is

$||r^{'} (t)|| = \sqrt{(1.4 t)^{2} + (3 (1 - t))^{2} + {(0.3 t^{2})}^{2}}$

$= \sqrt{1.96 t^{2} + 9 (1 + t^{2} - 2 t) + 0.09 t^{4}}$

$= \sqrt{1.96 t^{2} + 9 + 9 t^{2} - 18 t + 0.09 t^{4}}$

$= \sqrt{10.96 t^{2} + 9 - 18 t + 0.09 t^{4}}$

Hence, work done in carrying weight of $80$ pounds following the position of trail of $r (t) = <0.7 t^{2} + 1, 1.5 t (2 - t), 0.1 t^{3}>$ is $W = 80 {鈭�}_{0}^{1} \sqrt{10.96 t^{2} + 9 - 18 t + 0.09 t^{4}} d t$

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

Most popular questions from this chapter

Q. Examples: Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading.

(a) A smooth surface with a smooth boundary.

(b) A surface that is not smooth, but that has a smooth boundary.

(c) A surface that is smooth, but does not have a smooth boundary

Use the curl form of Green鈥檚 Theorem to write the line integral of F(x, y) about the unit circle as a double integral. Do not evaluate the integral.

Do the vectors in the range of $F (x, y) = x i + y j$ point towards or away from the origin?

In what way is Stokes鈥� Theorem a generalization of the Fundamental Theorem of Line Integrals?

The current through a certain passage of the San Juan Islands in Washington State is given by

$F = <F_{1} (x, y), F_{2} (x, y)> = <0, 1.152 - 0.8 x^{2}> .$

Consider a disk R of radius 1 mile and centered on this region. Denote the boundary of the disk by localid="1650455155947" $鈭� R$ .

(a) Compute localid="1650455166518" ${鈭�}_{R} (\frac{鈭� F_{2}}{鈭� x} - \frac{鈭� F_{1}}{鈭� y}) d A$ .
(b) Show that ${鈭�}_{鈭� R} F 路 n d s = {鈭�}_{0}^{2 蟺} (1.152 - 0.8 \cos^{2} 胃) \sin 胃 d 胃 .$ Conclude that Green's Theorem is valid for the current in this area of the San Juan Islands.
(c) What do the integrals from Green's Theorem tell us about this region of the San Juan Islands?

See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.