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CBSE Class 12-science Answered

A particle suffers 3 displacements by 4m in the northward,2m in the south-east and 2m in the south-west directions. What is the displacement of the particle?
Asked by kandappan | 19 Apr, 2020, 08:37: AM
answered-by-expert Expert Answer
Let us consider X-Y coordinate system so that X-axis in West-to-East direction and
Y-axis in South-to-North direction as shown in figure.
 
Let us assume initially the particle is at origin O.
 
First displacement to point A is 4m north, i.e.  4 begin mathsize 14px style j with hat on top end style m , where begin mathsize 14px style j with hat on top end style is a unit vector in y-direction.
Position vector of point A = 4 begin mathsize 14px style j with hat on top end style m
Second displacement is 2 m in the direction South-East to the point B .Hence displacement = √2 begin mathsize 14px style i with hat on top end style - √2 begin mathsize 14px style j with hat on top end style
Hence position vector of B  = ( 4 begin mathsize 14px style j with hat on top end style) + ( √2 begin mathsize 14px style i with hat on top end style - √2 begin mathsize 14px style j with hat on top end style) = √2 begin mathsize 14px style i with hat on top end style + ( 4 - √2 ) begin mathsize 14px style j with hat on top end style
Third displacement is 2 m in the direction south west to the point C .Hence displacement = -√2 begin mathsize 14px style i with hat on top end style - √2 begin mathsize 14px style j with hat on top end style
Hence position vector of C  = ( √2 begin mathsize 14px style i with hat on top end style + ( 4 - √2 ) begin mathsize 14px style j with hat on top end style ) + ( -√2 begin mathsize 14px style i with hat on top end style - √2 begin mathsize 14px style j with hat on top end style ) = ( 4 - 2√2 ) begin mathsize 14px style j with hat on top end style = 1.172 begin mathsize 14px style j with hat on top end style
Hence net displacement = 1.172 begin mathsize 14px style j with hat on top end style
Answered by Thiyagarajan K | 19 Apr, 2020, 12:52: PM

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