Question

A ball is thrown horizontally from the roof of a building 45cm tall and lands 24.0m from the base. What was the ball's initial velocity?

Answer 1

I'm going to assume you meant 45.0 m tall for the building (rather than cm).

Vertically (take upward as positive):
d = vit + (1/2)at ²
-45 = 0*t + (1/2)(-9.81)t ²
t ~ 3.0 s

Horizontally (take direction of throw as positive)
d = vit
24 = vi (3.0)
vi ~ 8 m/s

Answer 2

0.0m