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# The height of a flare fired from the deck of a ship in distress can be modeled by h= - 16t^2+ 104t+ 56, where h is the height in feet of the flare above water and t is the time in seconds. What is the time it takes the flare to hit the water?

Jan 11, 2017

t = 7 seconds

#### Explanation:

The flare hit the water when $h = 0$

$- 16 {t}^{2} + 104 t + 56 = 0$

divide the equation by 8,
$- 2 {t}^{2} + 13 t + 7 = 0$
$\left(- 2 t - 1\right) \left(t - 7\right) = 0$

$- 2 t - 1 = 0 , t = - \frac{1}{2}$

$t - 7 = 0 , t = 7$

since unit of time cannot be a -ve value, therefore t, time the flare hit the water is at 7s