A man standing at a window 5 meters tall watches a falling ball pass by the window in 0.3 seconds. From how high above the top of the window was the ball released?

11.76 meters.

Step-by-step explanation:

To carry out the problem it is necessary to take into account the following equations:

The first, in relation to the initial and final velocity, we know that gravity is 9.81 m / s ^ 2 and that the time is 0.3 seconds.

Vf = Vo + g * t = Vo + 9.81 * 0.3

Vf = Vo + 2.94 (1)

The second, in the same way relating the initial and final speed, also with gravity but this time with the distance S, which we know to be 5 meters.

Vf ^ 2 = Vo ^ 2 + 2 * g * S

Vf ^ 2 = Vo ^ 2 + 2 * 9.81 * 5

Vf ^ 2 = Vo ^ 2 + 98.1 (2)

Now, we have two equations with two unknowns. If we replace (1) in (2):

(Vo + 2,943) ^ 2 = Vo ^ 2 + 98.1

Vo ^ 2 + 5,886 * Vo + 8.66 = Vo ^ 2 + 98.1

Vo ^ 2 is canceled and we have, and reorganizing, we have:

Vo = 89.44 / 5.886

Vo = 15,195 m / s

Now with the following formula we will calculate the height

Vo ^ 2 = 2 * g * h

h = Vo ^ 2 / (2 * g) = (15,195 ^ 2) / (2 * 9.81) = 11.76 meters

In other words, the height corresponds to 11.76 meters.