The Physics Teacher Vol. 50, 2012

Physics Challenge for Teachers and Students

Boris Korsunsky, Column EditorWeston High School, Weston, MA 02493 korsunbo@post.harvard.edu

Solution to September 2012 Challenge

w A Futile ChaseTwo turtles, A and B, are relaxing at the waters edge a distance d apart. Then A begins to swim away from the shore. B gives chase, taking off at the same moment. During the chase, A keeps swimming directly away from the shore while B keeps swimming directly toward A. The speeds of both turtles are the same. Find the distance between A and B after a long time interval.

Solution: The figure above shows the position of both turtles t seconds after they start to swim. The speed of approaching each other is given by:

vapp = V V cos (a).

After a long time t (t ) the distance between the turtles is D, and we can write:

app0

d v dt

D= (1)

0[ cos( )] .d V V dt

D=

We can also write a similar condition in the y direction:

0cos( )V V dt

D=

(2) 0[ cos( )] .V V dt

D=

From Eqs. (1) and (2) we obtain: d D = D.Finally, the distance between the turtles is:

.2

dD=

(Contributed by Norge Cruz Hernndez, University of Seville, Spain)

Thanks to the following contributors:Konstantin Bogdanov (Lyceum #1586, Moscow, Russia)Phil Cahill (The SI Organization, Inc., Rosemont, PA)Don Easton (Lacombe, Alberta, Canada)Fredrick P. Gram (Cuyahoga Community College,

Cleveland, OH)Sicheng Guo, student (Jiangsu Tianyi High School,Wuxi,

Jiangsu, China) Charles Holbrow (Colgate University, Hamilton, NY)Jos Ignacio iguez de la Torre (Universidad de Salaman-

ca, Salamanca, Spain)Jarrett L. Lancaster (James Madison University, Harrison-

burg, VA)Gabriel Lisboa, student (Colgio Integrado Objetivo, So

Paulo, Brazil)Matthew W. Milligan (Farragut High School, Knoxville,

TN)Carl E. Mungan (U. S. Naval Academy, Annapolis,

MD) Jason L. Smith (Richland Community College, Decatur, IL)

Guidelines for contributors:

We ask that all solutions, preferably in Word format, be submitted to the dedicated email address challenges@aapt.org. Each message will receive an au-tomatic acknowledgment.

The subject line of each message should be the same as

A

d

v B

v

v

v

d

y

xt

the name of the solution file (see the instructions below).

The deadline for submitting the solutions is the last day of the corresponding month.

We can no longer guarantee that well publish every successful solvers name; each month, a representa-tive selection of names will be published, perhaps 10 to 15, both in print and on the web.

If your name isfor instanceKarl Mamola, please name the file Dec12Mamola (do not include your first initial) when submitting the December solu-tion.

If you have a message for the Column Editor, you may contact him at korsunbo@post.harvard.edu; however, please do not send your solutions to this address.

As always, we look forward to your contributions and hope that they will include not only solutions but also your own Challenges that you wish to sub-mit for the column.

Thank you and enjoy! Boris Korsunsky, Column Editor