2 dimensional motion problem

I am going to work this problem in two parts.  First, I am going to only deal with vertical components to find out how much time it takes the ball to reach the first step:

Knowns:

a = g = -9.81 m/s²

v_i= 0 m/s

x_i = 0 m

x_f = -.19 m

1/2at² + v_it + x_i = x_f

1/2(-9.81)t² + 0t + 0 = -.19

t² = 2*(-.19)/(-9.81)

t = .0387 s

Now, we will determine how far the ball traveled horizontally in this time.

Known:

v = 3.4 m/s

t = .0387 s

v = x/t

x = vt

x = 3.4*(.0387)

x = .132 m

Therefor, the ball strikes the top step.  It would have to travel .29 m horizontally before dropping .19 m vertically in order to not hit the top step.