Question 558914: 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)   (Show Source):
You can put this solution on YOUR website! 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.
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It hits the ground when h(t) = 0
h(t) = -9.8t2 – 10t + 270 = 0
Solve for t.
The units are seconds, as you stated.
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The equation is not right for Earth's gravity, tho.
It's -4.9t^2 – 10t + 270 = 0 not -9.8
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| Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=5392 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: -8.51328969415748, 6.47247336762686.
Here's your graph:
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Ignore the negative answer.
t =~ 6.47 seconds
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