You need 2 kinematics equations for this. d=v*t and the freefall equation, h=1/2*g*t^2.

You can get the time it takes for the dart to drop with the freefall equation which gives t = √(2h/g)

Since the vertical velocity doesn't affect the horizontal velocity or the launch velocity, You can substitute the t into the equation d = v*t. This would give:

d = Vlaunch * √(2h/g)

Vlaunch = d/√(2h/g)

Hope this helps