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 :
[tex]h= -16t^2 + 16t + 32[/tex]
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
[tex]-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[/tex]
Neglecting t = -1 seconds, the time taken by the flare to reach the ground is 2 seconds.