Question

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 of the flare above water and t is the time in seconds. Find the time it takes the flare to hit the water.

Answer 1

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 $h=-16t^2+104t+56$, 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 $h=0$ to find the time when ball will hit the ground as:

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

Using quadratic formula, we will get:  

$t=\frac{-104\pm\sqrt{104^2-4(-16)(56)}}{2(-16)}$

$t=\frac{-104\pm\sqrt{10816+3584}}{-32}$

$t=\frac{-104\pm\sqrt{14400}}{-32}$

$t=\frac{-104\pm120}{-32}$

$t=\frac{-104+120}{-32}\text{ or }t=\frac{-104-120}{-32}$

$t=\frac{16}{-32}\text{ or }t=\frac{-224}{-32}$

$t=-\frac{1}{2}\text{ or }t=7$

Since time cannot be negative, therefore, it will take 7 seconds for the flare to hit the ground.