1. Convert Units:

* Speed: 100 km/h needs to be converted to meters per second (m/s):

* 100 km/h * (1000 m/km) * (1 h/3600 s) = 27.78 m/s

2. Apply the Physics:

* We'll use the following kinematic equation:

* v² = u² + 2as

* where:

* v = final velocity (27.78 m/s)

* u = initial velocity (0 m/s, since it starts from rest)

* a = acceleration due to gravity (9.8 m/s²)

* s = distance (what we want to find)

3. Solve for Distance (s):

* Rearrange the equation to solve for 's':

* s = (v² - u²) / (2a)

* Substitute the values:

* s = (27.78² - 0²) / (2 * 9.8)

* s ≈ 39.5 m

Therefore, a 1.00 kg ball would have to fall approximately 39.5 meters to reach a speed of 100 km/h.

Important Note: This calculation neglects air resistance, which would significantly affect the actual distance required in real-world scenarios.