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Three particles start from the origin at the same time,one with a velocity u1       along x axis,the second along the y axis with a velocity u2 and the third along the x=y line.the velocity of the third so that the three may lie on the same line is??

Asked by Sunita 5th June 2019, 1:38 PM
Answered by Expert
Answer:
Let at instant of time t, particle Q has moved u1t m along x-axis and partcle P has moved u2t m along y-axis.
 
The line joining P and Q is   begin mathsize 14px style fraction numerator x over denominator u subscript 1 t end fraction space plus space fraction numerator y over denominator u subscript 2 t end fraction space equals space 1 end style .............................(1)

particle R is moving along the line,      y = x .....................(2)
 
if P, Q and R are in line at time t, then coordinate of R is the point of intersection of eqn.(1) and eqn.(2)
 
we get point of intersection as, begin mathsize 14px style x space equals space y space equals space alpha t space space comma space space space space w h e r e space space alpha space equals space fraction numerator u subscript 1 space u subscript 2 over denominator u subscript 1 space plus space u subscript 2 end fraction end style
Hence displacement OR at time t = √2 α t
 
Hence velocity of particle-R = √2 α = begin mathsize 14px style fraction numerator square root of 2 space u subscript 1 space u subscript 2 over denominator u subscript 1 space plus space u subscript 2 end fraction end style
 
Answered by Expert 5th June 2019, 9:32 PM
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