4.2 A treasure map you uncovered while vacationing on theSpanish Coast reads as

Question

4.2 A treasure map you uncovered while vacationing on theSpanish Coast reads as follows: "If me treasure ye wants, me hoardye'll have, just follow thee directions these. Step to the southfrom Brisbain's Mouth, 5 paces through the trees. Then to the west,10 paces ye'll quest, with mud as deep as yer knees. Then 3 pacesmore north, and dig straight down in the Earth, and me treasure,take it please." What is the displacement vector from Brisbain'sMouth to the spot on the Earth above the treasure? Consider eastthe positive x direction and north the positive ydirection.

(, ) paces

Explanation / Answer

. 01.   Directions to treasure: 02.      South 5 paces, then 03.      West 10 paces, then 04.      North 3 paces, then 05.      dig ! . 06.   I shall use "âx"and "ây" to denote East-directionand North-direction, respectively. . 07.   D = displacement vector= (-5 paces)ây + (-10paces)âx + (3paces)ây 08.   D = (-10paces)âx + (-2paces)ây 09.   |D| = { (-10paces)2 + (-2 paces)2}(1/2) = 10.198 paces 10.   D = arctan[(-2)/(-10)]= 11.31 degrees 11.   D = 10.198 paces 11.31 degrees South ofWest . 09.   |D| = { (-10paces)2 + (-2 paces)2}(1/2) = 10.198 paces 10.   D = arctan[(-2)/(-10)]= 11.31 degrees 11.   D = 10.198 paces 11.31 degrees South ofWest .

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