SOLUTION: how would you solve this problem and show work i'm trying to understand the concept, i have a test coming up soon.thank you Three novice sailors were attempting to sail to Cancu

Question 844676: how would you solve this problem and show work i'm trying to understand the concept, i have a test coming up soon.thank you
Three novice sailors were attempting to sail to Cancun mexico from fl during the Christmas break when a storm overtook them. the most composed of the sailors fired a shot with the flare gun straight up into the air hoping against hope that someone would see the distress signal. The height H of the flare, in meters above the "ground", t seconds after firing, can be modeled by the function: H(t)=-4.9t^2+166t+2.2
based on the height model, is it likely the sailor was sitting or standing in the raft when he fired the flare gun? How do you know?
give the height from which the flare was fired in meters?
give the maximum height reached by the flare?
How long did it take for the flare to reach the maximum height?
how long was the flare in the air?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The height H of the flare, in meters above the "ground", t seconds after firing, can be modeled by the function: H(t)=-4.9t^2+166t+2.2
based on the height model, is it likely the sailor was sitting or standing in the raft when he fired the flare gun? How do you know?
The flare was fired at t = 0
h(0) = 2.2 meters, not likely to be in a raft.
-----------------------------------
give the height from which the flare was fired in meters? 2.2 meters, see above.
----------------------------
give the maximum height reached by the flare?
Max height is the vertex of the parabola, at t = -b/2a
t = -166/-9.8 = 830/49 seconds =~16.939 seconds
h(830/49) = 1408.118 meters
--------------------------
How long did it take for the flare to reach the maximum height?
830/49 seconds
------------------------
how long was the flare in the air?
Neglect the 2.2 meters from the firing point --> 2*830/49 seconds
830/49 secs going up, same falling
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