pls solve the problem

Asked by mufeedatvp2000 | 18th Apr, 2020, 09:45: AM

Expert Answer:

Position vector of particle-1 ,  begin mathsize 14px style stack r subscript 1 with rightwards arrow on top space equals space 4 space i with hat on top space minus space 4 space j with hat on top space plus space 7 space k with hat on top space end style m ,
velocity of particle-1 ,   begin mathsize 14px style stack v subscript 1 with rightwards arrow on top space equals space 0.4 space i with hat on top space space end stylem/s ,
Position of the particle-1 after 10 s = begin mathsize 14px style stack r subscript 1 with rightwards arrow on top space plus space 10 space stack v subscript 1 with rightwards arrow on top space equals space 8 space i with hat on top space minus 4 j with hat on top space plus 7 space k with hat on top end style   m .............................(1)
Position vector of particle-2 ,  begin mathsize 14px style stack r subscript 2 with rightwards arrow on top space equals space 2 space i with hat on top space plus space 2 space j with hat on top space plus space 5 space k with hat on top space end style  m,
Let velocity of particle-2 ,   begin mathsize 14px style stack v subscript 2 with rightwards arrow on top space equals space a space i with hat on top space plus space b space j with hat on top space plus space c space k with hat on top space end stylem/s ,
Position of the particle-2 after 10 s is given by ,
 
begin mathsize 14px style stack r subscript 2 with rightwards arrow on top space plus space 10 space stack v subscript 2 with rightwards arrow on top space equals space left parenthesis 2 plus 10 a right parenthesis space i with hat on top space plus left parenthesis space 2 space plus space 10 b space right parenthesis j with hat on top space plus left parenthesis space 5 space plus space 10 c space right parenthesis space k with hat on top end style m ......................(2)
If both particle collide after 10s, then their position vectors are equal
 
Hence by equating (1) and (2), we get,  2+10a = 8 ,  2+10b = -4 and (5+10c) = 7
 
Hence we get a = 0.6 ,  b = -0.6  and  c = 0.2
 
Hence velocity of particle-2 ,   begin mathsize 14px style stack v subscript 2 with rightwards arrow on top space equals space 0.6 space i with hat on top space minus space 0.6 space j with hat on top space plus space 0.2 space k with hat on top space end style m/s
 

Answered by Thiyagarajan K | 18th Apr, 2020, 02:15: PM

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