Final answer:
To estimate the time it takes for a rock to fall 125 feet, we use the formula t = √(2s/g), arriving at approximately 2.8 seconds. However, this time doesn't match any of the provided options, suggesting there may be an error in the question or we could be dealing with a unique situation not covered by the basic free-fall model.
Step-by-step explanation:
To estimate how long it will take for a rock to reach the ground when it falls from a height of 125 feet, we can use the free-fall formula s = 1/2gt², where s is the distance fallen, g is the acceleration due to gravity (approx. 9.8 m/s² or 32 ft/s²), and t is the time in seconds. However, since the height given is in feet, we will use the value of g in feet per second squared for this calculation.
First, we need to convert the height to the same units of acceleration due to gravity, which is already in feet. The height is 125 feet, so no conversion is necessary. Now we rearrange the formula to solve for time t: t = √(2s/g).
t = √(2*125/32)
t = √(250/32)
t = √(7.8125)
t ≈ 2.8 seconds
Since we are estimating and none of the options are close to 2.8 seconds, it seems the given options might not be correct. Assuming the question meant to ask for a height that would yield one of the given time options, we could calculate which of those would be most fitting for the height of 125 feet.