While following a treasure map, you start at an old oak tree. You first walk 825
ID: 2166297 • Letter: W
Question
While following a treasure map, you start at an old oak tree. You first walk 825 directly south, then turn and walk 1.25 at 30.0 west of north, and finally walk 1.00 at 40.0 north of east, where you find the treasure: a biography of Isaac Newton!Part A
To return to the old oak tree, in what direction should you head ? Use components to solve this problem.
= ________ west of south degrees
Part B
To return to the old oak tree, how far will you walk? Use components to solve this problem.
= ______ m
Explanation / Answer
The first displacement is just south at 825 m
The second has components...
West = 1250(sin 30) = 625 m
North = 1250(cos 30) = 1082.5 m
The third also has components
East = (1000)(cos 40) = 766 m
North = (1000)(sin 40) = 642.8 m
In the horizontal, we have a total of 625 West and 766 East. That leaves a net of 766 - 625 = 141 m East
In the vertical, we have a total of 825 South, 1082.5 North and 642.8 North. That leaves a net of 1082.5 + 642.8 - 825 = 900.3 m North
Part 1)
The angle is found by tan = 900.3/141
= 81.1o North of East.
Thus, to return to the tree, head the other way, that is...
81.1o South of West (or you can call it 8.90o West of South)
Part 2)
The distance is found using the pythagorean theorem.
d = [(900.3)2 + (141)2]
d = 911.3 m
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