Find the resultant displacement from the cave entrance

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SUMMARY

The discussion focuses on calculating the resultant displacement of a spelunker who moves in various directions from a cave entrance. The movements include 75 m north, 250 m east, 100 m at a 30° angle north of east, and 160 m south. The calculations yield a resultant displacement magnitude of approximately 338.42 m, with an angle of -5.94° relative to the east direction. A discrepancy arises when the spelunker mistakenly uses 150 m south instead of 160 m, leading to confusion regarding the correct resultant values.

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Homework Statement


While exploring a cave, a spelunker starts at the entrance and moves the following distances. She goes 75 m north, 250 m east, 100 m at an angle 30° north of east, and 160 m south. Find the resultant displacement from the cave entrance.



Homework Equations





The Attempt at a Solution



So (75+100sin30- 160) = -35
and 250 + 100cos30 = 336.6025
magnitude =338.4173

Trying to find the angle and should be arctan(-35/336.6025)=-5.93629

Here's my problme though I accidently used 150 m south and blackboard gave me credit for 335.6729 m as my magnitude. Now who is wrong me or blackboard? I'm at lost as to which numbers to use now for my angle calculation.
 
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hi hawk24! :smile:

i'm surprised it didn't reject your answer as having too many sig figs …

maybe the correct answer is 340?
 

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