SOLUTION: A ball is thrown downward from a window in a tall building. Its position at time t in seconds is s = 16t2 + 32t, where s is in feet. How long (to the nearest tenth) will it take th

Algebra ->  Length-and-distance -> SOLUTION: A ball is thrown downward from a window in a tall building. Its position at time t in seconds is s = 16t2 + 32t, where s is in feet. How long (to the nearest tenth) will it take th      Log On


   

Question 949493: A ball is thrown downward from a window in a tall building. Its position at time t in seconds is s = 16t2 + 32t, where s is in feet. How long (to the nearest tenth) will it take the ball to fall 110 feet?
Found 2 solutions by Zucchini, Alan3354:
Answer by Zucchini(70) About Me  (Show Source):
You can put this solution on YOUR website!
Just plug in and solve:
110 = 16t + 32t
110 = 48t
2.3 = t

It will take 2.3 seconds for the ball to fall from 110 feet.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A ball is thrown downward from a window in a tall building. Its position at time t in seconds is s = 16t2 + 32t, where s is in feet. How long (to the nearest tenth) will it take the ball to fall 110 feet
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s = 16t2 + 32t
Use ^ (Shift 6) for exponents.
s = 16t^2 + 32t
s = 16t^2 + 32t = 110
16t^2 + 32t - 110 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 16x%5E2%2B32x%2B-110+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2832%29%5E2-4%2A16%2A-110=8064.

Discriminant d=8064 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-32%2B-sqrt%28+8064+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2832%29%2Bsqrt%28+8064+%29%29%2F2%5C16+=+1.80624304008046
x%5B2%5D+=+%28-%2832%29-sqrt%28+8064+%29%29%2F2%5C16+=+-3.80624304008046

Quadratic expression 16x%5E2%2B32x%2B-110 can be factored:
16x%5E2%2B32x%2B-110+=+%28x-1.80624304008046%29%2A%28x--3.80624304008046%29
Again, the answer is: 1.80624304008046, -3.80624304008046. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B32%2Ax%2B-110+%29

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t =~ 1.806 seconds
Ignore the negative solution.