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Question
A person moves 30 m north, then 30 m east, then 30 √2 m south-west. His displacement from the original position is:
A person moves 30 m north, then 30 m east, then 30 √2 m south-west. His displacement from the original position is:
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Solution
The correct option is A 10 m towards west
Given that,
A person moves 30m North then 20m east than 30√2 meter southwest.
The movement along north direction, Vector OY=30^j
The movement along east direction, Vector YX=20^i
Movement along south west direction,XZ=
30√2(cosθ^i+sinθ^j)
Vector XZ=30√2(cos45A0^i+sin45A0^j)=30i+30j
Using triangle vector law,
OX=20i+30j
XZ=30i+30j
In triangle XZO,OZ is resultant from origin.
OZ=OX−XZ
OZ=20i+30j−30i−30j
OZ=−10i
Hence, The position of person from origin is 10m West.
Given that,
A person moves 30m North then 20m east than 30√2 meter southwest.
The movement along north direction, Vector OY=30^j
The movement along east direction, Vector YX=20^i
Movement along south west direction,XZ=
30√2(cosθ^i+sinθ^j)
Vector XZ=30√2(cos45A0^i+sin45A0^j)=30i+30j
Using triangle vector law,
OX=20i+30j
XZ=30i+30j
In triangle XZO,OZ is resultant from origin.
OZ=OX−XZ
OZ=20i+30j−30i−30j
OZ=−10i
Hence, The position of person from origin is 10m West.
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