Answer:
the flare will be in the air for approximately 29.09 seconds before fizzling out at a height of 10 meters above ground.
Explanation:
To find out how long the flare will be in the air, we need to find the time it takes for the flare to reach a height of 10 meters.
Setting h(t) to 10 and solving for t:
-0.5t² +16t+22 = 10
-0.5t² +16t+12 = 0
Using the quadratic formula:
t = (-b ± √(b² - 4ac)) / 2a
Where a = -0.5, b = 16, and c = 12:
t = (-16 ± √(16² - 4(-0.5)(12))) / 2(-0.5)
t = (-16 ± √(256 + 24)) / -1
t = (-16 ± √280) / -1
t ≈ -1.09 or t ≈ 29.09
Since time cannot be negative, we can ignore the negative root. Therefore, the flare will be in the air for approximately 29.09 seconds before fizzling out at a height of 10 meters above ground.