worksheet5

worksheet5 - the bank twice and then returns to its...

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MA 1002 Worksheet 5 Due Date: October 7, 2009 Print Name: Signature: ID #: Instructor/Section: Instructions: Explain each step using the conventions from class. Please mark solutions clearly. You will not receive full credit for a correct answer without explanation. 1. (50 points) Use mathematical software (matlab, maple, mathematica) or an applet to determine the exact coordinates of all solutions to Alhazen’s Billiard problem given: r = 2 , A = ( - 1 , - 1) , B = (1 , - 1). Plot the corresponding circle and hyperbola into the same coordinate system and state their equations. 2. (50 points) Suppose you are given a circular Billiard table with one Billiard ball in a Fxed position. ±ind the direction in which to hit the ball such that it re²ects o³
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Unformatted text preview: the bank twice and then returns to its original position. 3. (extra) Consider the trajectory of a Billiard ball in a triangle (start at any point, in any direction, and assume that the speed remains constant. If the ball hits one of the corners, the ball stops). Can you play in such a way that the trajectory Flls the entire triangle? Can you play in such a way that a certain area of the triangle is never covered by the trajectory? Answer the same questions for a circle. You may want to use a java applet, e.g. the one on http://serendip.brynmawr.edu/chaos/doc.html....
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This note was uploaded on 12/09/2009 for the course MA 1002 taught by Professor N/a during the Spring '09 term at NYU Poly.

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