A sailor in a small sail boat encounter shifting winds. She sails 2.00km East , then 3.50km 45° Southeast, and then an additional distance in an unknown direction
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Expert's answer
2021-03-08T08:15:58-0500
Let vector a represents the displacement 2.0 km east and vector b represents the displacement 3.50 km southeast. Let's find the resultant displacement:
We can find the magnitude of the resultant displacement from the Pythagorean theorem:
R=Rx2+Ry2=(4.47km)2+(−2.47km)2=5.11km.
We can find the direction from the geometry:
θ=sin−1(RRy)=sin−1(5.11km−2.47km)=−28.9∘.
The sign minus means that the resultant displacement has direction 28.9∘SofE.
Now, let vector a represents the displacement 5.11 km 28.9∘SofE, vector b represents the unmeasured displacement which we are searching for, and vector R represents the final resultant displacement of the sailor - 5.80 km directly east of the starting point.
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