Can you please show work?

Question

A ball is thrown horizontally from the roof of a building 9.4 m tall and lands 9.4 m from the base. What was the ball's initial speed? Express your answer using two significant figures. 

Answer 1

To do this problem, you must think of the ball separately in each of the "y" and "x" directions.

In the y-direction:

Since the initial velocity is ONLY horizontal, then there is no initial velocity in the y-direction making the ball's travel in the y-direction exactly the same as if it were dropped. The kinematic equation y = v_y-it + 1/2at² is applicable but v_y-i = zero. So y = 1/2at² where "a" = g = 9.8 m/s² and y = 9.4:

9.4 = 1/2(9.8)t²

9.4(2)/9.8 = t²

t = 1.918 seconds

Meaning it takes the ball 1.918 seconds to reach the ground after having either been dropped from 9.4 m or having been thrown horizontally from 9.4m.

In the x-direction:

During the 1.918 seconds that the ball is dropping, the horizontal velocity remains at its initial velocity (there are no forces in the horizontal direction). The kinematic equation x = vt is applicable where "t" is 1.918 seconds and x = 9.4 m

9.4 = 1.918v

v = 9.4/1,918 = 4.9 m/s