SOLUTION: 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 6 foot tal

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 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 6 foot tal      Log On


   

Question 166107: 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 6 foot tall woman on a sidewalk looks directly overhead and sees a window washer drop a bottle from the 4 story. How long does she have to get out of the way? Round to the nearest tenth. (A story is 12 feet.) Choose the answer from the following:
2.0 seconds

1.5 seconds

1.6 seconds

1.3 seconds

Please help solve and show how to arrive at answer.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
First, you need to find the height (s) from which the bottle was dropped.
s+=+4%2812%29 This is 4 storeys times 12 ft per storey.
s+=+48feet.
The observer is 6 feet tall, so you want to find the time, t, at which the bottle reaches a height of 6 feet when dropped from a height (s) of 48 feet.
Starting with:
h%28t%29+=+s-16t%5E2 Substitute h = 6 ft. and s = 48 ft.
6+=+48-16t%5E2 Add 16t%5E2 to both sides.
16t%5E2%2B6+=+48 Subtract 6 from both sides.
16t%5E2+=+42 Divide both sides by 16.
t%5E2+=+42%2F16 Now take the square root of both sides.
t+=+sqrt%2842%2F16%29 Simplify the right side.
t+=+6.48%2F4
t+=+1.6 seconds.