What is the initial velocity of a ball that is thrown downward from the rooftop of a 12-m building and falls to the ground after 1.14 s. Ignore air...

We can solve this by using the equation of motion.

where s is the distance traveled, u is the initial velocity, t is the time duration and a is the acceleration. 

In this case, the distance traveled (s) is 12 meters. The time taken by the ball to fall down is 1.14 seconds and the acceleration is due to Earth's gravity and is, hence, equal to acceleration due to gravity, g. 

Thus, s = 12 m, t = 1.14 s and a = g = 9.81 m/s^2

Substituting these values into the equation of motion, we get:

12 = 1.14u + 1/2 (9.81) (1.14)^2

Solving the equation, we get, u = 4.94 m/s.

Thus, the ball was thrown with an initial velocity of 4.94 m/s.

Note that resistance by air has been neglected in this case.

Hope this helps.