The formula s=16t^2 is used to approximate the distance s, in feet, that an object falls freely from the rest in t seconds. The height of a building is

Question

The formula s=16t^2 is used to approximate the distance s, in feet, that an object falls freely from the rest in t seconds. The height of a building is 1473 feet. How long would it take for an object to fall from the top?

Answer 1

You want to see how long it will take an object to fall 1473 feet down to the ground.  These means its position s must be 1473.  By setting the equation equal to this value, we get:

 

1473 = 16t^2

 

Now, we have to solve for t.  First, divide both side by 16, getting:

 

1473/16 = 92.0625 = t^2  Now taking the square root of both sides, we get:

 

sqrt(92.0625) = 9.5949 seconds.