SOLUTION: Anna and Carly threw their math books out of a window that’s 36 feet from the ground. The equation of each textbook’s pathway is given below. Whose book will reach the ground first

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Anna and Carly threw their math books out of a window that’s 36 feet from the ground. The equation of each textbook’s pathway is given below. Whose book will reach the ground first      Log On


   

Question 1116127: Anna and Carly threw their math books out of a window that’s 36 feet from the ground. The equation of each textbook’s pathway is given below. Whose book will reach the ground first and by how many seconds?
Anna: h(t)= -16t^2 + 36
Carly: h(t)= -16t^2 + 10t + 36
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Anna and Carly threw their math books out of a window that’s 36 feet from the ground. The equation of each textbook’s pathway is given below. Whose book will reach the ground first and by how many seconds?
Anna: h(t)= -16t^2 + 36
Carly: h(t)= -16t^2 + 10t + 36
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Carly's book was thrown with an upward speed of 10 ft/sec, so it reach the ground last.
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Solve each equation for t to find the difference.
At impact, h(t) = 0
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Anna: h(t)= -16t^2 + 36 = 0
t = sqrt(36/16) = 3/2 seconds
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Carly: h(t)= -16t^2 + 10t + 36 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B10x%2B36+=+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=%2810%29%5E2-4%2A-16%2A36=2404.

Discriminant d=2404 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-10%2B-sqrt%28+2404+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2810%29%2Bsqrt%28+2404+%29%29%2F2%5C-16+=+-1.21970633401641
x%5B2%5D+=+%28-%2810%29-sqrt%28+2404+%29%29%2F2%5C-16+=+1.84470633401641

Quadratic expression -16x%5E2%2B10x%2B36 can be factored:
-16x%5E2%2B10x%2B36+=+%28x--1.21970633401641%29%2A%28x-1.84470633401641%29
Again, the answer is: -1.21970633401641, 1.84470633401641. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B10%2Ax%2B36+%29

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Ignore the negative value
t =~ 1.8447 seconds, vs 1.5 seconds