Given a CFG $G=(V_N, V_T, R, S)$ and one of its nonterminals $v$ determine if there exists a production chain $S \Rightarrow^* v \alpha$?

I am supposed to find an algorithm solving the following problem:

Given a CFG $$\;G=(V_N, V_T, R, S)$$ and a nonterminal $$v \in V_N$$ determine if there exists a production chain $$S \Rightarrow^* v \alpha$$, where $$\alpha = (V_N + V_T)^*$$.

Not sure if that’s the right term, but in other words we are trying to check if you can yield $$v$$ from $$S$$ – the starting symbol.

I don’t know anything about the form of the grammar and I can’t convert it into Chomsky’s form as it would introduce new nonterminals and possibly remove $$v$$. Where do I start with this? Any suggestions?

Thanks