Unformatted text preview: T H E C A R P E T R I D E P R O B L E M : T A S K S 1 A N D 2 You are a traveler, leaving home for the first time. To aid you on your journey, you receive two gifts. Specifically, two forms of transportation: a hover board and a magic carpet. Both the hover board and the magic carpet have restrictions in how they operate: "3%
!!# 1& Hoverboard: We denote the restriction on the hover board’s movement by the vector $ ' . By this we mean that if the hover board traveled “forward” for one hour, it would move along a “diagonal” path that would result in a displacement of 3 units East and 1 unit North €
of its starting location. " 1% Magic Carpet: We denote the restriction on the magic carpet’s movement by the vector $ ' . 2
!!# & By this we mean that if the magic carpet traveled “forward” for one hour, it would move along a “diagonal” path that would result in a displacement of 1 unit East and 2 units North €
of its starting location. SCENARI0 ONE: THE MAIDEN VOYAGE Your Uncle Cramer suggests that your first adventure should be to go visit the wise man, Old Man Gauss. Uncle Cramer tells you that Old Man Gauss lives in a cabin that is 107 units East and 64 units North of your home. TASK: Investigate whether or not you can use the hover board and the magic carpet to get to Gauss’s cabin. If so, how? If it is not possible to get to the cabin with these modes of transportation, why is that the case? As a group, state and explain your answer(s) on the white board in such a way that allows you to present it to the class. Use the vector notation for each mode of transportation as part of your explanation. Use a diagram or graphic if it helps illustrate your point(s). SCENARIO TWO: HIDE-‐AND-‐SEEK Each week Old Man Gauss moves his cabin to a different location. You are not sure whether Gauss is just trying to test your wits at finding him or if he actually wants to hide somewhere that you can't visit him. Are there some locations that he can hide and you cannot reach him with these two modes of transportation? Describe the places that you can reach using a combination of the hover board and the magic carpet and those you cannot. Specify these geometrically and algebraically. Include a symbolic representation using vector notation. Also, include an argument for why you are correct. Zandieh, MAT 343, Fall 2015.
Adapted from the IOLA materials: © IOLA Team - iola.math.vt.edu. ...
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