homework and exercises - Point charge moving towards a conducting plane

A point charge $q$ of mass $m$ is released from rest at a distance $d$ from an infinite grounded conducting plane. Show that the charge hits the plane after an amount of time given by:

$\Delta t= \frac{\pi d} {q} \sqrt{2\pi\epsilon_0md}$

I can't seem to start this one. I'm assuming I need to start by finding the force by the charge as a function of $z$, and setting it equal to $\frac{md^2z}{dt}$ giving a differential equation. The diff eq. seems hard to solve, but a hint I recieved was to multiply both sides by $\frac{dz}{dt}$, but I don't see how this simplifies the problem.