Question

The height of a flare fired from a 32-foot high platform can be modeled by the function h= -16t^2 + 16t + 32, where h is the height in feet above the ground and t is the time in seconds. Find the time it takes the flare to reach the ground

Answer 1

Answer:

Time, t = 2 seconds

Step-by-step explanation:

The height of a flare fired from a 32-foot high platform can be modeled by the function :

$h= -16t^2 + 16t + 32$

Here, h is the height in feet above the ground and t is the time in seconds.

It is required to find the time taken by the flare to reach the ground. When its reaches ground, height covered by it equals 0 such that,

h = 0

$-16t^2 + 16t + 32=0\\\\t=\dfrac{-16+\sqrt{16^2-4\times (-16)(32)} }{2(-16)}, \dfrac{-16-\sqrt{16^2-4\times (-16)(32)} }{2(-16)}\\\\t=-1\ s, 2\ s$

Neglecting t = -1 seconds, the time taken by the flare to reach the ground is 2 seconds.