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10meast 12m north 4m south 4m West find the displacement

Asked by anjjuchalla7 28th October 2023, 8:31 PM
Answered by Expert
Answer:
Graphical method :-
 
Above graph shows Displacements made at different direction.
 
Initially the object is at A . First displacement AB of magnitude 10 m is made towards East .
 
Then BC of magnitude 12 m is made towards north. Nex displacement is CD of magnitude 4 m towards south.
 
Final displacement is DE of magnitude 4 m towards west .
 
Net displacement from starting position to final position is AE . If we measure the magnitude of AE ,
we find that net displacement AE is of magnitude 10 m .
 
If we measure the direction angle θ from graph ,
 
we find that  tanθ = 8/6 or θ = tan-1 ( 4/3 ) = 53o
 
Hence the net displacement is 10 m in the direction 53o north of east
 
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Vector method :-
 
Let direction towards East is the direction of x-axis . Let direction towards north is direction of y-axis as shown in figure.
 
Let begin mathsize 14px style i with hat on top space end stylebe the unit vector along x-axis and begin mathsize 14px style j with hat on top space end stylebe the unit vector along y-axis .
Displacement AB = begin mathsize 14px style stack A B with rightwards arrow on top space equals space left parenthesis space 10 space m space right parenthesis space i with hat on top space end style;
Displacement BC = begin mathsize 14px style stack B C with rightwards arrow on top space equals space left parenthesis space 12 space m space right parenthesis space j with hat on top space end style;
Displacement CD = begin mathsize 14px style stack C D with rightwards arrow on top space equals space minus left parenthesis space 4 space m space right parenthesis space j with hat on top space end style
Displacement DE = begin mathsize 14px style stack D E with rightwards arrow on top space equals space minus left parenthesis 4 space m space right parenthesis space i with hat on top space end style
Net displacement = begin mathsize 14px style stack A E with rightwards arrow on top space equals space stack A B with rightwards arrow on top plus stack B C with rightwards arrow on top plus stack C D with rightwards arrow on top plus stack D E with rightwards arrow on top end style = begin mathsize 14px style left parenthesis space 6 space space m space right parenthesis space i with hat on top space plus space left parenthesis space 8 space m space right parenthesis space j with hat on top end style
magnitude of begin mathsize 14px style stack A E with rightwards arrow on top end style = begin mathsize 14px style square root of 8 squared plus 6 squared end root space m space equals space 10 space m end style
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Answered by Expert 29th October 2023, 9:35 AM
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