SOLUTION: Can you please help me solve this story problem. A ball is thrown downward from a window in a tall building. It's position at time t in seconds is s=16t^2+32t, where s is in feet.

Question 476276: Can you please help me solve this story problem. A ball is thrown downward from a window in a tall building. It's position at time t in seconds is s=16t^2+32t, where s is in feet. How long (to the nearest tenth) will it take the ball to fall 217 feet? I took 217=16t^2+32t = -217 = 16t^2+32t-217=0 I did a=16, b=32, and c= -217. I used the formula -b+-√b^2-4ac/2a I got -32+-√14,912/32. I'm lost from that point on to get the answer. I have the answer key it says it's 2.8 seconds. Can you help me complete this? Thanks.
Found 2 solutions by scott8148, bucky:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
you want the positive value for your solution

[-32 + sqrt(14912)] / 32

this should work on your calculator
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
You have completed the problem correctly. Your equation:
.
You need to recognize that in solving the equation by using the quadratic formula as you did, you are solving for t. In other words you got as far as:
.

.
and that is correct up to that point. Good job!!!
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Now let's finish up the problem. Note that if you use the - sign in front of the radical that you will have two negatives in the numerator ... namely negative 32 and negative the radical. This means that the answer for t will be negative. But that's meaningless. Negative time doesn't make sense. You need to get a positive answer. That means that you should forget about the negative sign that precedes the radical and just use the positive sign. So let's do that. The equation becomes:
.

.
Use a calculator to find the square root of 14912. You will find that it is 122.1147 and this makes the equation become:
.

.
Add the two terms in the numerator:
.

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Now do the division using a calculator and you get:
.

.
This rounds off to
.
And that's the answer in seconds that you were given by the answer key.
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You were so close because you worked the problem correctly down to the final stage. Job well done on a difficult problem!!!

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