Word Problem for the formula: h = s - 16t^2

[flora33]

All right, here is a word problem that I am having trouble putting together the equation...

The height h (in feet) of an object that is dropped from the height of s feet is given by the formla 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 3rd 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:

1.8 seconds
1.5 seconds
1.4 seconds
1.1 seconds

36 = 30 - 16t^2 Is this correct? I multiplied 3 stories by 12 feet and that is h, or the height of an object that is dropped. Then for s I did the same as for h, except subtracted the height of the 6-foot tall woman. The sentence, "The height h (in feet) of an object that is dropped from the height of s feet..." seems redundant and doesn't make sense when I read it. To me it is saying that h and s are both the height in feet that an object is dropped, but that can't be right. Any input is greatly appreciated.

Flora

 

[Mrspi]

The height h (in feet) of an object that is dropped from the height of s feet is given by the formla 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 3rd story. How long does she have to get out of the way? Round to the nearest tenth. (A story is 12 feet).

The bottle is dropped from a height of 36 feet...and that is the value of s:

h = 36 - 16t^2

"h" is the height of the dropped object above the ground after t seconds. Since the woman is 6 feet tall, the bottle will hit her at 6 feet above the ground. That is the value of h.

6 = 36 - 16t^2

Now....solve that for t. She doesn't have a lot of time to get out of the way!

 

[TchrWill]

The height h (in feet) of an object that is dropped from the height of s feet is given by the formla 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 3rd story. How long does she have to get out of the way? Round to the nearest tenth. (A story is 12 feet).

At 12 feet per story, the floor of the 3rd story is 24 feet above the groun (1st story at ground level).
Assuming the worker is also 6 feet tall, his feet are at the floor level of the 3rd floor and he drops the bottle with his arm outstretched in a horizontal position, his arm would be ~5 feet above the floor level.
Assuming that if the woman was standing, the object would hit the top of her head, 6 feet above the ground.

Then, s would equal 2(12) + 5 - 6 = 23 feet.

Then, 23 = 16t^2 making t = 1.989 sec.

Assuming s = 36 feet is the only way you can get 1.4 sec.

If the worker dropped the object from floor level, the time would be 1.06 sec.

The description of the scenario requires more speific details.

 

[flora33]

Thank you both for your input. It was a great help!

Flora