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.

Algebra ->  Quadratic Equations and Parabolas -> 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.       Log On


   

Question 476328: 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?
Found 2 solutions by jorel1380, stanbon:
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
16t2+32t=217
16t2+32t-217=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 16x%5E2%2B32x%2B-217+=+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-217=14912.

Discriminant d=14912 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-32%2B-sqrt%28+14912+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2832%29%2Bsqrt%28+14912+%29%29%2F2%5C16+=+2.81608438061844
x%5B2%5D+=+%28-%2832%29-sqrt%28+14912+%29%29%2F2%5C16+=+-4.81608438061844

Quadratic expression 16x%5E2%2B32x%2B-217 can be factored:
16x%5E2%2B32x%2B-217+=+16%28x-2.81608438061844%29%2A%28x--4.81608438061844%29
Again, the answer is: 2.81608438061844, -4.81608438061844. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B32%2Ax%2B-217+%29

The two answers are 2.81608438061844, -4.8160843806184. Throwing out the negative answer, we get t=2.816..

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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?
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Solve:
16t^2+32t = 217
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t = [-32 +- sqrt(32^2-4*16*-217)]/(2*32)
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t = [-32 +- 122.11]/64
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Positive solution:
t = 1.41 seconds
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Cheers,
Stan H.