SOLUTION: If a ball is thrown vertically upward from a height of 5 ft, with an initial velocity of 96 ft/s, its height h after t seconds is given by h = -16t^2 + 96t + 5. How long does it ta

Algebra ->  Rectangles -> SOLUTION: If a ball is thrown vertically upward from a height of 5 ft, with an initial velocity of 96 ft/s, its height h after t seconds is given by h = -16t^2 + 96t + 5. How long does it ta      Log On


   



Question 313615: If a ball is thrown vertically upward from a height of 5 ft, with an initial velocity of 96 ft/s, its height h after t seconds is given by h = -16t^2 + 96t + 5. How long does it take the ball to pass through a height of 120 ft on the way back down to the ground?

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If a ball is thrown vertically upward from a height of 5 ft, with an initial velocity of 96 ft/s, its height h after t seconds is given by h = -16t^2 + 96t + 5. How long does it take the ball to pass through a height of 120 ft on the way back down to the ground?
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h = -16t^2 + 96t + 5
120 = -16t^2 + 96t + 5 solve for t
-16t^2 + 96t + 5 = 120
-16t^2 + 96t + -115 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B96x%2B-115+=+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=%2896%29%5E2-4%2A-16%2A-115=1856.

Discriminant d=1856 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-96%2B-sqrt%28+1856+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2896%29%2Bsqrt%28+1856+%29%29%2F2%5C-16+=+1.65370879821637
x%5B2%5D+=+%28-%2896%29-sqrt%28+1856+%29%29%2F2%5C-16+=+4.34629120178363

Quadratic expression -16x%5E2%2B96x%2B-115 can be factored:
-16x%5E2%2B96x%2B-115+=+%28x-1.65370879821637%29%2A%28x-4.34629120178363%29
Again, the answer is: 1.65370879821637, 4.34629120178363. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B96%2Ax%2B-115+%29

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t = 1.65 seconds going up
t = 4.346 seconds falling