What is the meeting point of two objects - the former moving across a path with constant speed, and latter with constant speed and undefined path

Question

This is an exact equivalent of my question, can someone re-write the accepted answer in more simplified terms/notation? i.e what does gamma represent? etc..

Answer 1

Join the line from $A$ to $C$ and let angle $BAC=\beta$. Let the direction of particle $C$ be defined by the angle $\alpha$ it makes with the line $CA$. In this set-up, the angle $\beta$ and the speeds $U_1$ and $U_2$ are known, but the angle $\alpha$ needs to be determined.

In order for the particles to meet, they must be at the same perpendicular distance from the line $AC$ at the same time. Therefore the components of velocity perpendicular to the line $AC$ must be equal and therefore we solve for $\alpha$ the equation $$U_1\sin\beta=U_2\sin\alpha$$.

As was pointed out by @RoryDaulton, there are often two solutions for $\alpha$ depending on the other numbers involved, and obviously there may be situations where interception is impossible - i.e. no real solution for $\alpha$.