Answer
$x\approx.889m$
Work Step by Step
We first solve for time:
$t=\sqrt {\frac{2x}{g}}=\sqrt \frac{2(2.00m)}{(9.8m/s^{2})}=.639s$
The second droplet has been falling for two thirds of the time: $t_{2}=\frac{2(.639s)}{3}=.426s$
We use the equation for distance to obtain:
$x=\frac{1}{2}(9.8m/s^{2})(.426s)^{2}\approx.889m$
