SOLUTION: If a penny is thrown downward at 30 ft/sec from the bridge at Royal Gorge, Colorado, how long does it take to reach the Arkansas River 1000 ft below? It says to use the quadra

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: If a penny is thrown downward at 30 ft/sec from the bridge at Royal Gorge, Colorado, how long does it take to reach the Arkansas River 1000 ft below? It says to use the quadra      Log On


   

Question 209449: If a penny is thrown downward at 30 ft/sec
from the bridge at Royal Gorge, Colorado, how long does it
take to reach the Arkansas River 1000 ft below?
It says to use the quadratic equation.

x^2-〖30〗^2=〖1000〗^2
I have work started but it's not pasting into here.
It's from my online textbook, I cannot find the ISBN.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If a penny is thrown downward at 30 ft/sec
from the bridge at Royal Gorge, Colorado, how long does it
take to reach the Arkansas River 1000 ft below?
It says to use the quadratic equation.
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The height of an object (neglecting air friction) is
h(t) = -16t^2 + vt + h0 Where v is the starting speed and h0 is the initial height. t is in seconds, h in feet.
In this case h0 = 1000 ft, and v = -30 ft/sec (-30 since it's thrown downward)
Find when h(t) = 0
0 = -16t^2 - 30t + 1000
-8t^2 - 15t + 500 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -8x%5E2%2B-15x%2B500+=+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=%28-15%29%5E2-4%2A-8%2A500=16225.

Discriminant d=16225 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--15%2B-sqrt%28+16225+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-15%29%2Bsqrt%28+16225+%29%29%2F2%5C-8+=+-8.89858700178562
x%5B2%5D+=+%28-%28-15%29-sqrt%28+16225+%29%29%2F2%5C-8+=+7.02358700178562

Quadratic expression -8x%5E2%2B-15x%2B500 can be factored:
-8x%5E2%2B-15x%2B500+=+%28x--8.89858700178562%29%2A%28x-7.02358700178562%29
Again, the answer is: -8.89858700178562, 7.02358700178562. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-8%2Ax%5E2%2B-15%2Ax%2B500+%29

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Use the positive value for t (it says x2)