SOLUTION: Aubrey uses a slingshot to shoot a marble from a window. The height of the marble h(t) in feet at time t seconds is given by the function h(t)=-16t square -50t+164. How many second

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Aubrey uses a slingshot to shoot a marble from a window. The height of the marble h(t) in feet at time t seconds is given by the function h(t)=-16t square -50t+164. How many second      Log On


   

Question 371009: Aubrey uses a slingshot to shoot a marble from a window. The height of the marble h(t) in feet at time t seconds is given by the function h(t)=-16t square -50t+164. How many seconds elapse before the marble hits the ground?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
h(t)=-16t square -50t+164
When it reaches the ground the "height" is zero
so, set h(t) to zero and solve for t:
0=-16t^2 -50t+164
0=16t^2 + 50t - 164
0=8t^2 + 25t - 82
Applying the "quadratic formula" we find that
t = {2, -5.125}
Throw out the negative answer leaving
t = 2 seconds
.
Details of quadratic to follow:
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case 8t%5E2%2B25t%2B-82+=+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=%2825%29%5E2-4%2A8%2A-82=3249.

Discriminant d=3249 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-25%2B-sqrt%28+3249+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%2825%29%2Bsqrt%28+3249+%29%29%2F2%5C8+=+2
t%5B2%5D+=+%28-%2825%29-sqrt%28+3249+%29%29%2F2%5C8+=+-5.125

Quadratic expression 8t%5E2%2B25t%2B-82 can be factored:
8t%5E2%2B25t%2B-82+=+8%28t-2%29%2A%28t--5.125%29
Again, the answer is: 2, -5.125. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B25%2Ax%2B-82+%29