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boy a is standing at a point 3 m west and 4 m south to boy b. assume the east and the north towards the positive x and y axis of coordinate system. boy a starts moving along a vector a =1.5 i +2 j with a constant speed of 2m/s for 5 seconds and stops. now how far is the boy a from the boy b

Asked by nutankumari95074 12th June 2022, 1:28 PM
Answered by Expert
Answer:
 
Let us consider boy B is standing at origin . Initially boy-A is 3 m west and 4 m south .
 
hence initial coordinate of boy-A = ( -3 m , -4 m )
 
Boy-A is travelling in the direction of vector  v =  ( 1.5 i + 2.0 j )
 
Unit vector  begin mathsize 14px style v with hat on top end style along the direction of vector v is given as
begin mathsize 14px style v with hat on top equals space fraction numerator 1.5 over denominator square root of left parenthesis 1.5 right parenthesis squared plus 2 to the power of 2 end exponent end root end fraction stack i space with hat on top space plus space fraction numerator 2.0 over denominator square root of left parenthesis 1.5 right parenthesis squared plus 2 squared end root end fraction j with hat on top space equals space 0.6 space i with hat on top space plus 0.8 space j with hat on top end style
 
If boy-A travels with speed 2 m/s for 5 s , then magnitude of displacement 10 m
 
Displacement vector from initial position of boy-A = 10 ( 0.6 i + 0.8 j ) m = ( 6 i + 8 j ) m
 
Hence boy-A has diplaced 6 m towards east and 8 m towards north.
 
Hence final coordinates of boy-A = ( -3+6 m , -4+8 m ) = ( 3m , 4 m )
 
Distance between boy-A and boy-B = begin mathsize 14px style square root of 3 squared plus 4 squared end root space m space equals space 5 space m end style
Answered by Expert 12th June 2022, 5:33 PM
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