SOLUTION: Amir pitched a baseball at an initial height of 5.9 feet with a velocity of 73.16 feet per second. About how long will it take the ball Amir pitched to hit the ground?

Algebra ->  Algebra  -> Quadratic Equations and Parabolas -> SOLUTION: Amir pitched a baseball at an initial height of 5.9 feet with a velocity of 73.16 feet per second. About how long will it take the ball Amir pitched to hit the ground?      Log On

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Question 616574: Amir pitched a baseball at an initial height of 5.9 feet with a velocity of 73.16 feet per second. About
how long will it take the ball Amir pitched to hit the ground?
Answer by Alan3354(30993) About Me  (Show Source):
You can put this solution on YOUR website!
Amir pitched a baseball at an initial height of 5.9 feet with a velocity of 73.16 feet per second. About
how long will it take the ball Amir pitched to hit the ground?
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The equation commonly used is
h%28t%29+=+-16t%5E2+%2B+vt+%2B+h where v = vertical speed and h = initial height
h%28t%29+=+-16t%5E2+%2B+73.16t+%2B+5.9
At impact, h(t) = 0
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h%28t%29+=+-16t%5E2+%2B+73.16t+%2B+5.9+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B73.16x%2B5.9+=+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=%2873.16%29%5E2-4%2A-16%2A5.9=5729.9856.

Discriminant d=5729.9856 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-73.16%2B-sqrt%28+5729.9856+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2873.16%29%2Bsqrt%28+5729.9856+%29%29%2F2%5C-16+=+-0.0792708860840778
x%5B2%5D+=+%28-%2873.16%29-sqrt%28+5729.9856+%29%29%2F2%5C-16+=+4.65177088608408

Quadratic expression -16x%5E2%2B73.16x%2B5.9 can be factored:
-16x%5E2%2B73.16x%2B5.9+=+%28x--0.0792708860840778%29%2A%28x-4.65177088608408%29
Again, the answer is: -0.0792708860840778, 4.65177088608408. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B73.16%2Ax%2B5.9+%29

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Ignore the negative solution
t =~ 4.652 seconds