Final answer:
To calculate the time it takes for the ball to reach the ground, kinematic equations for free-fall under gravity are used. Without the height given in the question, it's impossible to select a correct option confidently. A hypothetical example using a height of 98 meters results in a time of approximately 4.47 seconds.
Step-by-step explanation:
To determine how long it takes for a ball to reach the ground when dropped from a certain height, we can use kinematic equations for free-fall motion under the influence of gravity, with g = 9.8 m/s². The formula to use is s = ut + ½gt², where s is the displacement, u is the initial velocity, t is the time, and g is the acceleration due to gravity. Since the ball is dropped from rest, u = 0 and the formula simplifies to s = ½gt².
We need to rearrange the equation to solve for t, giving us t = √(2s/g). Without the height of the building given in the options (A) through (D), we cannot calculate the exact time. To find an actual numerical result, the height from which the ball is dropped is necessary. For educational purposes, let's assume a height; however, this is purely hypothetical as the actual value is not provided in the question.
Assuming the building is 98 meters high, as one of the example questions suggests, we can calculate the time using t = √(2×98/g), which approximately gives us t = √(2×98/9.8) = √20 ≈ 4.47 seconds, falling between options B and C. But remember, without the actual height given within the specific question, you cannot confidently select one of the provided time options.