SOLUTION: "While surveying a cave, a spelunker follows a passage 190 m straight west, then 210 m in a direction 45.0° east of south, and then 270 m at 30.0° east of north. After a fourth u
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Question 1161805: "While surveying a cave, a spelunker follows a passage 190 m straight west, then 210 m in a direction 45.0° east of south, and then 270 m at 30.0° east of north. After a fourth unmeasured displacement, she finds herself back where she started. Use vector components to find the magnitude and direction of the fourth displacement." (Direction is requested as degrees west of south)
I already found the magnitude of the resultant vector to be 127 m. However, my theta value was incorrect and the "west of south" is tripping me up. Could someone help?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
We start from point ,
moving 190 units West along the negative x-axis to point
The components of vector are
and .
We reach
From there we go 210 units to point in a direction to the East of .
That is counterclockwise from the positive x-axis.
and .
The coordinates of are
and
Then we head to point for units
in a direction that is to the East of .
That is counterclockwise from the positive x-axis.
and .
The coordinates of are
and .
Finally we head back to starting point .
The distance of that fourth displacement is
The angle that makes with the positive x-axis is such that
and
The angle the direction makes with the direction is
and the direction is to the West of .
It forms a counterclockwise angle of with the positive x-axis
For verification:
The components of vector are
and
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