Hannah K.

asked • 03/16/17

Algebra 1 story problem

the  height h (in feet) above  the water of a cliff diver is modeled by h= -16t^2 +10t + 26,  where t is the time (in seconds).  How long is a diver in the air?

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Arturo O. answered • 03/16/17

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Solve the quadratic equation for t.
 
-16t2 + 10t + 26 = 0
 
t = (-1/32) {-10 ± √[102 - 4(-16)(26)]} = (-10 ± 42) / (-32) = -1 or 1.625 seconds
 
The negative result is not physically possible, so the time is the positive result, i.e. 1.625 s
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Carl F. answered • 03/16/17

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Hannah, 
 
What would the height of the diver be when she hits the water? How can you use that information in the equation?
 
David Finley
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Hannah K.

I do not understand 
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03/16/17

Carl F.

The diver is getting closer and closer to the water as she dives, right? How many feet above the water will she be when she is no longer in the air?
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03/16/17

Hannah K.

I have no clue
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03/16/17

Carl F.

If you are in the water, how far from the water are you? 
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03/16/17

Hannah K.

0 feet
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03/16/17

Carl F.

Exactly! What can you do with that information in the equation?
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03/16/17

Hannah K.

Can u put 0 for the hight 
 
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03/16/17

Carl F.

Yes!
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03/16/17

Hannah K.

So I did that but my an doesn't make since.   -13,-2
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03/16/17

Carl F.

How did you solve for t?
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03/16/17

Hannah K.

These were my steps
0=-16t^2 + 10t + 26
(-8x+13)(2x+2)
       -13       -2
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03/16/17

Carl F.

You almost got it! You forgot to divide -13 by -8 and -2 by 2. Only one of those answers works in the real world.
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03/16/17

Carl F.

Does that help you get the solution?
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03/16/17

Hannah K.

So does -2/2 or -1 the one that works....because I got 32 seconds for and answer
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03/16/17

Carl F.

 -1 second is one answer, but as Arturo said, that's impossible. The other answer is (-13)/(-8) = 13/8 seconds or 1.625 seconds.
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03/16/17

Carl F.

I was trying to let you do the thinking on this one, Hannah! :)
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03/16/17

Hannah K.

Thank you so much
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03/16/17

Carl F.

You are very welcome. If you find the need for a tutor in the future, you can always request a lesson from one of us.
 
Have a great night!
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03/16/17

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