Final answer:
The ball takes approximately 1.43 seconds to fall from the roof to the ground 25 feet below, using the formula for distance under constant acceleration due to gravity.
Step-by-step explanation:
To determine how long it takes for the ball to fall from the roof to the ground 25 feet below, we'll use the formula that comes from the equations of motion under constant acceleration (gravity). The equation for the distance (s) the object has travelled under the influence of gravity (g) is:
s = (1/2) × g × t^2
For an object in free fall near the surface of the Earth, the acceleration due to gravity (g) is approximately 32.2 feet/s^2. We can rearrange the formula to solve for time (t) and plug in the given distance:
25 = (1/2) × 32.2 × t^2
Solving for t gives us:
t ± 1.43 seconds
Therefore, the approximate time it takes for the ball to fall 25 feet to the ground is 1.43 seconds (C).