akldhf a.

asked • 03/02/17

The height h (in feet) above the water of a cliff diver is modeled by h=−16t^+8t+80, where t is the time (in seconds). How long is the diver in t

If you could help me solve this question that would be great! 
 
Thank you!

Debdatta B.

The question is not clear, how long the diver is in t ? do you mean air ?
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03/02/17

No Y.

How long in air, and i saw this question and Jason W. was on the right track, but the entire answer is 2.5, im a student who just did a BIM and got the answer of 2.5, so i mean, there u go
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02/22/21

Ashlin J.

The answer is 2.5 seconds but could someone explain step by step what they did to get that
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03/06/21

Elaina S.

They got 2.5 seconds because: 1) h=height t=seconds/time 2) h=-16t^2 + 8t + 80 3) because 8 is the greatest common factor and the leading coefficient is negative, you are going to want to divide everything by -8 so you get - 8 ( 2t^2 - t - 10 ) 4) you can use whatever method you want to factor that polynomial (I used the box method which is easiest for me) - 8 ( 2t^2 - t - 10 ) ---> t x 2t = 2t^2 2 x -5 = -10 2t x 2 = 4t t x -5 = -5t 5) 2t^2 + 4t - 5t - 10 = - 8 ( t + 2)( 2t - 5 ) ~you're finding how long the dive is in the air so you want to put the equation into t=0 and t=0 ~you're not going to distribute the -8 6) t + 2 = 0 and 2t - 5 = 0 ~time can't be negative and you want to make sure that it's not in fraction form ~t + 2 = 0 would give you t=-2 so that doesn't work 7) 2t - 5 = 0 ---> +5 2t = 5 ------ 2 t = 5/2 or 2.5 8) which gives you your answer. The diver was in the air for 2.5 seconds.
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02/02/22

1 Expert Answer

By:

Jason W. answered • 03/02/17

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4.8 (4)

Georgia Tech PhD student for Physics and Statistics

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I'm assuming you are asking how long is the diver in the air before hitting the water below. I also assume the equation is:
 
h = -16t2 + 8t + 80
 
So, factor out the GCF and factor the polynomial
 
h = 8*(-2t2 + t + 10)
h = 8*(-2t + 5)*(t + 2)
 
At t=0 the diver is at the top of the cliff, or h = 80 feet. At the bottom of the cliff, h = 0 feet. So,
 
0 = 8*(-2t + 5)*(t + 2)
 
Solve for t and remember that time can't be negative.
 
-2t + 5 = 0
t + 2 = 0
 
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