Anyway, I can provide u a solution in cartesian co-ordinates .
see, the controlling differential eqns are clearly.........
dx/dt = u cos
..................... ( 1 ) dy/dt = usin .......................( 2 ) y/( x - vt) = tan ....................... ( 3 )
y = - r sin .................. ( 4 ) Now the task is to solve these coupled differential eqn .
From ( 3 ) we have
x - vt = y cot dwrt 't'
dx/dt -v = dy/dt cot - y cosec^2() d/dt
combining ( 1 ) & ( 2 ) with this eqn we have
u cos - v = u sin cos /sin + r cosec d/dt or , d/dt = -v/r sin .................. ( A )
differentiating ( 4 ) wrt 't ' , we get
u sin = - d/d ( r sin ) d/dt
combining with ( A ) we get
or , u/v cosec - cot = 1/r dr/d
Now integrating it and putting the boundary condition that r= d at = 
/2
we get
r/d = ( 1- cos ) ^u/v / ( sin ) ^ ( u/v + 1 )
Moderation Team
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