A person moves 30, m north and then 20, m towards east and finally 30√ 2 ,m in south-west d

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3-2.Motion in Plane

medium

A person moves $30\, m$ north and then $20\, m$ towards east and finally $30\sqrt 2 \,m$ in south-west direction. The displacement of the person from the origin will be

A$10\, m$ along north

B$10 \,m $ along south

C$10\, m$ along west

D$Zero$

Solution

(c) From figure, $\overrightarrow {OA} = 0\;\overrightarrow i + 30\;\overrightarrow j $, $\overrightarrow {AB} = 20\;\overrightarrow i + 0\;\overrightarrow j $
$\overrightarrow {BC} = – 30\sqrt 2 \;cos{45^o}\overrightarrow i $$ – 30\sqrt 2 \;\sin {\rm{4}}{{\rm{5}}^{\rm{o}}}\overrightarrow j $ $ = – 30\;\overrightarrow i – 30\;\overrightarrow j $
Net displacement, $\overrightarrow {OC} = \overrightarrow {OA} + \overrightarrow {AB} + \overrightarrow {BC} $$ = – 10\;\overrightarrow i + 0\;\overrightarrow j $
$|\overrightarrow {OC} |\; = 10\;m.$

Standard 11

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(AIPMT-2002)

A person moves $30\, m$ north and then $20\, m$ towards east and finally $30\sqrt 2 \,m$ in south-west direction. The displacement of the person from the origin will be

Solution

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