Answer
$v_0 = 256~m/s$
Work Step by Step
We can find an expression for $v_x$:
$tan~\theta = \frac{v_{0y}}{v_x}$
$v_x = \frac{v_{0y}}{tan~\theta}$
We can find an expression for the time of flight:
$x = v_x~t$
$t = \frac{x}{v_x}$
$t = \frac{x}{\frac{v_{0y}}{tan~\theta}}$
$t = \frac{x~tan~\theta}{v_{0y}}$
We can find $v_{0y}$:
$y = v_{0y}~t+\frac{1}{2}a_y~t^2$
$y = v_{0y}~\frac{x~tan~\theta}{v_{0y}}+\frac{1}{2}(a_y)~(\frac{x~tan~\theta}{v_{0y}})^2$
$y -x~tan~\theta = \frac{a_y~(x~tan~\theta)^2}{2~v_{0y}^2}$
$v_{0y}^2 = \frac{a_y~(x~tan~\theta)^2}{2~(y-x~tan~\theta)}$
$v_{0y} = \sqrt{\frac{a_y~(x~tan~\theta)^2}{2~(y-x~tan~\theta)}}$
$v_{0y} = \sqrt{\frac{(-9.8~m/s^2)~(9400~m)^2~(tan~35^{\circ})^2}{(2)~(-3300~m-(9400~m)~tan~35^{\circ})}}$
$v_{0y} = 146.57~m/s$
We can find $v_0$:
$sin~\theta = \frac{v_{0y}}{v_0}$
$v_0 = \frac{v_{0y}}{sin~\theta}$
$v_0 = \frac{146.57~m/s}{sin~35^{\circ}}$
$v_0 = 256~m/s$
