How long does she have to get out of the way?

Question

The height h (in feet) of an object that is dropped from the height of s feet is given by the formula h = s - 16t 2 , where t is the time the object has been falling. A 4 foot tall woman on a sidewalk looks directly overhead and sees a window washer drop a bottle from the 2 story. Round to the nearest tenth. (A story is 12 feet.)

Answer 1

Since the bottle is dropped from the second story, and a story is 12 feet, the initial height of the bottle is 24 feet.

The question is asking when the bottle will hit her. Since she's 4 feet tall (kind of short huh?) that will be when the bottle is 4 feet above the ground.

So you are looking for t when h = 4:

h = s - 16t²
4 = 24 - 16t²
-20 = -16t²
20/16 = 5/4 = t²
t = √5/2 seconds or about 1.118 seconds to get out of the way. (1.1 seconds rounded to the nearest tenth.)