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.
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