Calculating Initial Velocity of a Basketball Shot

[Mgh3]

1. Problem
a basketball player is standing 9.5m from the basket which is at a height of 3.1m. She throws the ball from an initial height of 2.0m at an angle of 35 degrees above horizontal. The ball goes straight through the basket. Find v initial

2. Equations
Any range / Kinematic equations

3. My work
I tried separating the problem into x and y components, then used
-2 = Vi sin 35 + (1/2) * g * t^2
and
dx = Vi cos 35 * t

But this kept giving me incorrect answers.

 

[NasuSama]

Your equations are mostly correct, but you forget the $t$ variable next to $v_i\sin(35^{\circ})$. That is because the $y$-component distance formula is $y(t) = y_0 + v_i\sin(\theta)t + \dfrac{1}{2}gt^2$. Be sure to first express in that form.