Answer
$1.78m/s$
Work Step by Step
We can find the initial speed of the rock as follows:
$t_s=\frac{d}{v}=\frac{8.85}{343}=0.0258s$
and $t_f=1.20s-0.0258s=1.1742s$
Now $v_{\circ}=\frac{y-y_{\circ}}{t_f}-\frac{1}{2}at_f$
We plug in the known values to obtain:
$v_{\circ}=-\frac{8.85}{1.1742}-\frac{1}{2}(-9.81)(1.1742)$
$v_{\circ}=-1.78\frac{m}{s}$
The negative sign shows us that the initial velocity of the rock is downward.
