SOLUTION: I would greatly appreciate any help on the following problem: An object is projected upward from the top of a tower. Its distance in feet above the ground after t seconds is given

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Question 43881This question is from textbook
: I would greatly appreciate any help on the following problem: An object is projected upward from the top of a tower. Its distance in feet above the ground after t seconds is given by s(t)=-16t^2+64t+80. How many seconds will it take to reach ground level? This question is from textbook

Answer by aaaaaaaa(138) About Me  (Show Source):
You can put this solution on YOUR website!
Ground level is 0 feet, so it's a quadratic equation:
-16t%5E2%2B64t%2B80+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case -16t%5E2%2B64t%2B80+=+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=%2864%29%5E2-4%2A-16%2A80=9216.

Discriminant d=9216 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-64%2B-sqrt%28+9216+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%2864%29%2Bsqrt%28+9216+%29%29%2F2%5C-16+=+-1
t%5B2%5D+=+%28-%2864%29-sqrt%28+9216+%29%29%2F2%5C-16+=+5

Quadratic expression -16t%5E2%2B64t%2B80 can be factored:
-16t%5E2%2B64t%2B80+=+-16%28t--1%29%2A%28t-5%29
Again, the answer is: -1, 5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B64%2Ax%2B80+%29


We only want the positive solution, which is 5 seconds.