Respuesta :
Answer:
7 seconds.
Step-by-step explanation:
We have been given that the height of a flare fired from the deck of a ship in distress can be modeled by [tex]h=-16t^2+104t+56[/tex], where h is the height of the flare above water and t is the time in seconds.
The ball will hit the ground, when height will be 0 meters, so we will equate [tex]h=0[/tex] to find the time when ball will hit the ground as:
[tex]-16t^2+104t+56=0[/tex]
Using quadratic formula, we will get:
[tex]t=\frac{-104\pm\sqrt{104^2-4(-16)(56)}}{2(-16)}[/tex]
[tex]t=\frac{-104\pm\sqrt{10816+3584}}{-32}[/tex]
[tex]t=\frac{-104\pm\sqrt{14400}}{-32}[/tex]
[tex]t=\frac{-104\pm120}{-32}[/tex]
[tex]t=\frac{-104+120}{-32}\text{ or }t=\frac{-104-120}{-32}[/tex]
[tex]t=\frac{16}{-32}\text{ or }t=\frac{-224}{-32}[/tex]
[tex]t=-\frac{1}{2}\text{ or }t=7[/tex]
Since time cannot be negative, therefore, it will take 7 seconds for the flare to hit the ground.
