Question

The formula S=16t^2 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 1221 feet . How long would it take for an object to fall from the top

Answer 1

H(t)=-16t^2+1221 is the function for the height as a function of time.  It will hit the ground when h=0 so:

-16t^2+1221=0

16t^2-1221=0

16t^2=1221

t^2=1221/16

t=√(1221/16) seconds

t≈8.74 seconds  (to nearest hundredth of a second)

Answer 2

S=16t^2
1221=16t^2
1221/16=t^2
square root of 76.3=t
t=8.7