Chases and Escapes: The Mathematics of Pursuit and Evasion

By Paul J. Nahin | Go to book overview

Appendix A
Solution to the Challenge Problems of Section 1.1

Our first question is easy to answer. To calculate the distance sailed by the pirate ship until it captures the merchant vessel (n < 1), simply recall from (1.1.12) that capture occurs at (xo, n/(1 − n2)xo), i.e., the merchant has traveled a distance of n/(1 − n2)xo. Since the pirate ship travels 1/n times faster than does the merchant, the pirate travels 1/n times as far, that is, the pirate ship travels a total distance of 1/(1 –n2)xo.

To answer the second question, i.e., to determine the distance the pirate ship lags behind the merchant vessel after a long time has passed (for n = 1), refer to figure A. There we see the pirate ship at point (x,y), while the merchant vessel is at (xo, ym). Note, carefully, that this is for any arbitrary time t. The distance separating the pirate ship and the merchant vessel is D, where

Now, here’s the crucial observation: the line joining (x,y) to (xo, ym) is the tangent to the pirate’s pursuit curve, precisely because the chase

-187-

Notes for this page

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items
Notes
Cite this page

Cited page

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Note: primary sources have slightly different requirements for citation. Please see these guidelines for more information.

Cited page

Bookmark this page
Chases and Escapes: The Mathematics of Pursuit and Evasion
Table of contents

Table of contents

Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this book

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Help
Full screen
Items saved from this book
  • Bookmarks
  • Highlights & Notes
  • Citations
/ 254

matching results for page

    Questia reader help

    How to highlight and cite specific passages

    1. Click or tap the first word you want to select.
    2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
    3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

    OK, got it!

    Cited passage

    Style
    Citations are available only to our active members.
    Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

    1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

    Cited passage

    Thanks for trying Questia!

    Please continue trying out our research tools, but please note, full functionality is available only to our active members.

    Your work will be lost once you leave this Web page.

    Buy instant access to save your work.

    Already a member? Log in now.

    Search by... Author
    Show... All Results Primary Sources Peer-reviewed

    Oops!

    An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.