THE PHYSICS TEACHER ◆ Vol. 50, 2012 Physics Challenge for Teachers and Students Boris Korsunsky, Column Editor Weston High School, Weston, MA 02493 [email protected] Solution to September 2012 Challenge w A Futile Chase Two turtles, A and B, are relaxing at the water’s 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: v app = V – V cos (a). After a long time t (t ➝ ) the distance between the turtles is D, and we can write: app 0 d v dt τ −D= ∫ (1) 0 [ cos( )] . d V V dt τ α −D= − ∫ We can also write a similar condition in the y direction: 0 cos( ) V V dt τ τ α D= − ∫ (2) 0 [ cos( )] . V V dt τ α D= − ∫ From Eqs. (1) and (2) we obtain: d – D = D. Finally, the distance between the turtles is: . 2 d D= (Contributed by Norge Cruz Hernández, 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) José Ignacio Íñiguez de la Torre (Universidad de Salaman- ca, Salamanca, Spain) Jarrett L. Lancaster (James Madison University, Harrison- burg, VA) Gabriel Lisboa, student (Colégio Integrado Objetivo, São 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 [email protected]. 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 x t