Seconds to fall

Question

The formula S= 167 is used to approximate the distance S, in feet, that an object falls freely from rest in t seconds. The height of a building is 1099 feet. How long would it take for an object to fall from the top?

the object would fall for _ seconds?

Answer 1

Your question says "The formula S= 167 is used to approximate the distance S, in feet, that an object falls freely from rest in t seconds" and is in error. I'm going to assume the question is "The formula S = -16t² is used to approximate the distance S, in feet, that an object falls freely from rest in t seconds"

The height is the distance the object falls so S = -1099 feet:

S = -16t²

-1099 = -16t²

1099 = 16t²

1099/16 = t²

68.6875 = t²

t = √68.6875

t = 8.29 seconds