Let after time "t" the Position of A and B are in such a way that A is heading to B and its velocity makes some angle with x axis
So the relative speed of A with respect to B in horizontal direction is given as
[tex]\frac{dx}{dt} = u - vcos\theta[/tex]
relative motion in y direction is given as
[tex]\frac{dy}{dt} = 0 - vsin\theta[/tex]
from first equation we can say
[tex]\int dx = \int u dt - \int vcos\theta dt[/tex]
[tex]0 = uT - v\int cos\theta dt[/tex]
[tex]\int cos\theta dt = \frac{uT}{v}[/tex]
now in the direction of approach of each other
[tex]\frac{dr}{dt} = ucos\theta - v[/tex]
[tex]\int dr = \int ucos\theta dt - \int vdt[/tex]
[tex]0 - d = u\int cos\theta dt - vT[/tex]
[tex]- d = u(\frac{uT}{v}) - vT[/tex]
[tex]T = \frac{vd}{v^2 - u^2}[/tex]
