velocity of 3 particles on different axis for colinear position

Dear Student
After a time t 
 position of particle 1=  (u1t,0)
 position of particle 2=  (0, u2t)
 position of particle 3=  (   ut cos(45),-ut sin(45)  )

Say a line joining these points
Y=mx+c;
m=-u2t/u1t
Substitute m in the line eqn

c=y-mx
to get C use point 1
c=0-(-u2t/u1t)u1t=u2t
point 3 must satisfy the line equation to be on the line.

-ut sin(45)=(-u2t/u1t)ut cos(45)+u2t                      [ sin(45)= cos(45)=1/sqrt2]

(ut/sqrt2)[-1+(u2t/u1t)]=u2t  
(ut/sqrt2)= u2t  /  [-1+(u2t/u1t)]
u= (u2t  /  [-1+(u2t/u1t)]}t sqrt2

u=t^2 sqrt2 u1u2/(u1-u2)

Regars
Team
Topperlearning.com