Final answer:
Using the formula S=16t² for free falling objects and substituting the height of 1497 feet for S, the calculation reveals that it would take approximately 9.67 seconds for an object to fall from the top of the building.
Step-by-step explanation:
To calculate how long it would take for an object to fall from the top of a 1497 feet high building, we use the formula S=16t², where S is the distance in feet and t is the time in seconds. Given that the height of the building is 1497 feet, we can set up the equation 1497 = 16t², which we need to solve for t to find the time it takes for the object to fall.
First, we divide both sides by 16 to isolate t², yielding t² = 93.5625. Taking the square root of both sides gives us t ≈ 9.67 seconds. Therefore, it would take approximately 9.67 seconds for the object to fall from the top of a 1497 feet high building.