Question

The formula equals 16t squared 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 1437 feet. how long would it take for an object to fall from the​ top?

Answer 1

The equation is actually $h(t)=-16t^2+1437$.  Free fall is always -16t^2 as the position function.  We are looking for how long it takes the object to hit the ground.  In other words, the height of an object is 0 when it is laying on the ground, so how long (t) did it take to get there? We will then set that position equal to 0 and solve for t.  $0=-16t^2+1437$.  If we subtract 1437 from both sides and divide by -16, we have $t^2=89.8125$.  Taking the square root of both sides gives us, rounded to the nearest tenth, t = 9.5 or t=-9.5.  The 2 things in math that will never EVER be negative are time and distance/length, so -9.5 is out.  That means that it took just about 9.5 seconds for the object to fall to the ground from a height of 1437 feet when pulled on by the force of gravity.