SOLUTION: If a stone is tossed from the top of a 350 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 350, where t is in seconds, and height is

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Question 387697: If a stone is tossed from the top of a 350 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 350, 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 nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
h(t) = -9.8t2 – 10t + 350
Set h(t) to 0 and solve for t:
0 = -9.8t2 – 10t + 350
0 = -4.9t2 – 5t + 175
t = {-6.51, 5.49}
Only the positive answer makes sense:
t = 5.49 seconds
.
details of quadratic:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case -4.9t%5E2%2B-5t%2B175+=+0) has the following solutons:

t%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=%28-5%29%5E2-4%2A-4.9%2A175=3455.

Discriminant d=3455 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+3455+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+3455+%29%29%2F2%5C-4.9+=+-6.50808653456555
t%5B2%5D+=+%28-%28-5%29-sqrt%28+3455+%29%29%2F2%5C-4.9+=+5.48767837130024

Quadratic expression -4.9t%5E2%2B-5t%2B175 can be factored:
-4.9t%5E2%2B-5t%2B175+=+-4.9%28t--6.50808653456555%29%2A%28t-5.48767837130024%29
Again, the answer is: -6.50808653456555, 5.48767837130024. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4.9%2Ax%5E2%2B-5%2Ax%2B175+%29