Kinematics Problem: Find Constant Separation of Ships

[f(x)]

Homework Statement

There are two ships separated by a distance \gamma along a straight coastline. Ship A starts moving perpendicularly to the coastline , and Ship B moves such that its velocity vector always point along the position of Ship A.
Both ships move at same constant speed. After sufficient time, both the ships will move in a straight line with a constant separation. Find this separation.

2. MY ATTEMPT

First, i assumed the constant speed to be v
and let, after time T, both of them move in a straight line.
and let \theta be the angle that the velocity vector of ship B makes with that of the other. (\theta is variable from \pi / 2 \ \rightarrow \ 0 ) . I feel tan\theta \ = \ \frac{\gamma}{vt}

Then \gamma \ = \ v \ sin \theta \times T
and x \ = \ T (v-vcos \theta)

x= constant separation when ships are in a straight line

The problem is, I am unable to get differential equations which i should. How do i convert the known data into differential form ?

Any help is appreciated

 

[GoldPheonix]

I don't know a lot about differential equations, but I will say that velocity is the derivative of x(t). If you can figure out the position, maybe you can solve for the T variable. Or perhaps you could work this out like an optimization problem?

 

[f(x)]

Any means of solving this apart from what I've tried ?