SOLUTION: If a stone is tossed from the top of a 270 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 270, where t is in seconds, and height is

Algebra ->  Square-cubic-other-roots -> SOLUTION: If a stone is tossed from the top of a 270 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 270, where t is in seconds, and height is      Log On


   

Question 624960: If a stone is tossed from the top of a 270 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 270, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground? Round to the nearest hundredth’s place; include units in your answer.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
h(t) = -9.8t2 – 10t + 270
It hits the ground then h = 0
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h(t) = -9.8t2 – 10t + 270 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -9.8x%5E2%2B-10x%2B270+=+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=%28-10%29%5E2-4%2A-9.8%2A270=10684.

Discriminant d=10684 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+10684+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+10684+%29%29%2F2%5C-9.8+=+-5.78384879976431
x%5B2%5D+=+%28-%28-10%29-sqrt%28+10684+%29%29%2F2%5C-9.8+=+4.763440636499

Quadratic expression -9.8x%5E2%2B-10x%2B270 can be factored:
-9.8x%5E2%2B-10x%2B270+=+%28x--5.78384879976431%29%2A%28x-4.763440636499%29
Again, the answer is: -5.78384879976431, 4.763440636499. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-9.8%2Ax%5E2%2B-10%2Ax%2B270+%29

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t = x
Ignore the negative solution.
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t = 4.76 seconds
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Gravitional acceleration on Earth =~ 9.8 meters/sec/sec
The equation for the vertical position should be:
h(t) = -4.9t^2 – 10t + 270
not -9.8t^2
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It might be -9.8t^2 on some other planet somewhere, but not here.