Answer
The answer is
$$v_0=2.6\text{ m/s}.$$
Work Step by Step
The pumpkin has to travel the horizontal distance of $l=3.5\text{ m}$ and the vertical distance of $h=9\text{ m}$. Let $v_0$ be the initial speed, and $t$ the time of flight.
1) Since the launch velocity is horizontal we have
$$l=v_0 t\Rightarrow t=\frac{l}{v_0}.$$
2) Also, because the vertical initial component of the velocity is zero we have
$$h=\frac{1}{2}gt^2$$.
Plugging in for $t$ we get
$$h=\frac{1}{2}g\frac{l^2}{v_0^2}\Rightarrow v_0^2=\frac{gl^2}{2h}.$$
Taking the square root we get
$$v_0=l\sqrt{\frac{g}{2h}}=3.5\text{ m}\sqrt{\frac{9.81\text{ m/s}^2}{2\cdot9\text{ m}}}=2.6\text{ m/s}.$$
