There are two particles A and B which are moving with constant speed $v$ and $u$ such that $v$ is always directed towards B. At $t = 0$, the separation between A and B is $l$ and $u$ is perpendicular to the line joining A and B. The Velocity of B is constant i.e., it does not change its direction. Also $v>u$. Find the time when they will collide.
Here's my approach
The angle which A makes with the horizontal changes continuously from $0$ to $\theta$(let). At any time the angle which $v$ makes with horizontal will be a function of time. So $\alpha = f(t) $ where $\alpha$ lies from $0$ to $\theta$. Let time when they will collide be $t$ sec. So, $$\int_0^t v\cos(f(t)) dt = l$$ And $$\int_0^t v\sin(f(t)) dt = ut$$ Now I am stuck what to do next