Solution
= Solution
The <central force> conserves <angular momentum>. The initial impact parameter gives $L=ub$, while at closest approach the velocity is transverse and $L=wp$. Thus $u=wp/b$. <Conservation of energy> gives
$$
\frac{u^2}{2}-\frac{k}{R}
=\frac{w^2}{2}-\frac{k}{p}.
$$
Under $u^2\gg2k/R$, neglect the initial potential term and substitute $u=wp/b$:
$$
\frac{w^2p^2}{2b^2}
=\frac{w^2}{2}-\frac{k}{p}.
$$
Consequently
$$
\boxed{\frac{w^2}{k}
=\frac{2b^2}{p(b^2-p^2)}}.
$$