SOLUTION: 6.8 #17 Can someone please walk me through this? Before a football game, a coin toss is used to determine which team will kick off. The height h (in feet) of a coin above the

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: 6.8 #17 Can someone please walk me through this? Before a football game, a coin toss is used to determine which team will kick off. The height h (in feet) of a coin above the      Log On

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Question 231484: 6.8 #17
Can someone please walk me through this?
Before a football game, a coin toss is used to determine which team will kick off. The height h (in feet) of a coin above the ground t seconds after being flipped up into the air is given by the following equation.
h = -16t2 + 22t + 20.
How long does a team captain have to call heads or tails if it must be done while the coin is in the air?
____ seconds
Thank you,
Alan
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
h = -16t2 + 22t + 20.
How long does a team captain have to call heads or tails if it must be done while the coin is in the air?
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He has until it hits the ground, at h(t) = 0
-16t2 + 22t + 20 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B22x%2B20+=+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=%2822%29%5E2-4%2A-16%2A20=1764.

Discriminant d=1764 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-22%2B-sqrt%28+1764+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2822%29%2Bsqrt%28+1764+%29%29%2F2%5C-16+=+-0.625
x%5B2%5D+=+%28-%2822%29-sqrt%28+1764+%29%29%2F2%5C-16+=+2

Quadratic expression -16x%5E2%2B22x%2B20 can be factored:
-16x%5E2%2B22x%2B20+=+%28x--0.625%29%2A%28x-2%29
Again, the answer is: -0.625, 2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B22%2Ax%2B20+%29

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The solver uses x, that's the time t.
t = 2 seconds. (Ignore the negative number)

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
Formula is:

h = -16t^2 + 22t + 20.

The amount of time he gets to call heads or tails is the amount of time that the coin is in the air.

The coin is in the air until h = 0.

At that point in time, the coin has touched the ground.

You need to solve your equation for:

-16t2 + 22t + 20 = 0

Factor out a 2 from each coefficient to get:

-8t^2 + 11t + 10 = 0

Factors for this equation should be:

(8t + 5) * (-t + 2)= 0

You get:

-t = -2 which becomes t = 2

or you get:

8t = -5 which you reject right away because it's negative, and t can't be negative.

Your answer should be t = 2

This means that he gets 2 seconds to call heads or tails before the coin hits the ground.

To test, replace t in the original equation with 2 and you should get h = 0

h = -16t2 + 22t + 20 becomes:

h = -16*4 + 22*2 + 20 = -64 + 44 + 20 = -64 + 64 = 0

It checks out so your answer is 2 seconds.

There is a more complicated answer but I don't think it's pertinent to the exercise so, for practical purposes, you can ignore that, and just use the formula as I showed you above.