Question 844676
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.
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give the height from which the flare was fired in meters? 2.2 meters, see above.
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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
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How long did it take for the flare to reach the maximum height?
830/49 seconds
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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