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

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) (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.
---
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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1833 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.0683265857120221, 2.74417341428798. Here's your graph:

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

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