SOLUTION: A football is punted from a height of 2.5 feet above the ground with an initial vertical velocity of 45 feet per second. Write an equation to model the height h in feet of the b

Algebra ->  Functions -> SOLUTION: A football is punted from a height of 2.5 feet above the ground with an initial vertical velocity of 45 feet per second. Write an equation to model the height h in feet of the b      Log On


   

Question 971832: A football is punted from a height of 2.5 feet above the ground with an initial vertical velocity of 45 feet per second.
Write an equation to model the height h in feet of the ball t seconds after it has been punted.
The football is caught at 5.5 feet above the ground. How long was the football in the air?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A football is punted from a height of 2.5 feet above the ground with an initial vertical velocity of 45 feet per second.
Write an equation to model the height h in feet of the ball t seconds after it has been punted.
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32 ft/sec/sec is often used for gravity on Earth
--> h(t) = -16t^2 + 45t + 2.5
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The football is caught at 5.5 feet above the ground. How long was the football in the air?
h(t) = -16t^2 + 45t + 2.5 = 5.5
-16t^2 + 45t - 3 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B45x%2B-3+=+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=%2845%29%5E2-4%2A-16%2A-3=1833.

Discriminant d=1833 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-45%2B-sqrt%28+1833+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2845%29%2Bsqrt%28+1833+%29%29%2F2%5C-16+=+0.0683265857120221
x%5B2%5D+=+%28-%2845%29-sqrt%28+1833+%29%29%2F2%5C-16+=+2.74417341428798

Quadratic expression -16x%5E2%2B45x%2B-3 can be factored:
-16x%5E2%2B45x%2B-3+=+%28x-0.0683265857120221%29%2A%28x-2.74417341428798%29
Again, the answer is: 0.0683265857120221, 2.74417341428798. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B45%2Ax%2B-3+%29

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t =~ 0.068 seconds ascending thru 5.5 ft
t =~ 2.744 seconds when caught