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A particle starts from the point of origin (10m 37° North of East ) and then turns 4m towards north then turns 5m 37° North of West! Where is the distance traveled and the displacement found by partical ??

Asked by surabhilakhara7299 24th May 2021, 8:00 AM
Answered by Expert
Answer:
Graphical method.
 
Let us consider scale factor 1 cm = 5 m to draw the graph of displacement vectors.
 
We start from origin and draw vector OA of lenth 5 cm that makes angle 37o with x-axis .
Vector OA represents the displacement of 10 m in the direction 37o North of East .
 
Next draw a vector AB of length 2 cm starting from A in the direction of y-axis.
Vector OB represents the displacement of 4 m in North .
 
Next draw a vector BC of length 2.5 cm starting from B that makes angle 37o with -x axis.
Vector BC represents the displacement of 5 m in the direction 37o North of west.
 
 
 
Net displacement  from graph = 6.8 cm that equals 13.6 m real displacement
 
Total distance = ( 10 + 4 + 5 ) = 19 m
 
-------------------------------------------------------------
 
Vector method by resolving components
 
begin mathsize 14px style stack O A with rightwards arrow on top end style = ( 10 cos37 begin mathsize 14px style i with hat on top end style + 10 sin37 begin mathsize 14px style j with hat on top end style ) m

begin mathsize 14px style stack A B with rightwards arrow on top end style = 4 begin mathsize 14px style j with hat on top end style m
begin mathsize 14px style stack B C with rightwards arrow on top end style = -5 cos37 begin mathsize 14px style i with hat on top end style + 5 sin37 begin mathsize 14px style j with hat on top end style
begin mathsize 14px style stack O C with rightwards arrow on top end style = begin mathsize 14px style stack O A with rightwards arrow on top end style + begin mathsize 14px style stack A B with rightwards arrow on top end style + begin mathsize 14px style stack B C with rightwards arrow on top end style =  [ 5 cos37 begin mathsize 14px style i with hat on top end style + ( 15 sin37 + 4 ) begin mathsize 14px style j with hat on top end style ] m =  ( 4 begin mathsize 14px style i with hat on top end style + 13 begin mathsize 14px style j with hat on top end style ) m
| begin mathsize 14px style stack O C with rightwards arrow on top end style | = begin mathsize 14px style square root of 4 squared plus 13 squared end root space equals space 13.6 space m end style
Total distance = ( 10 + 4 + 5 ) = 19 m  
Answered by Expert 24th May 2021, 11:43 AM
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