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A flare is launched from a life raft at initial velocity of 80 meters per second.
How many seconds will it take the flare to fall back to the sea ?
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As it was written in the post, the condition was INCOMPLETE, since the direction of the launch was not specified.
THEREFORE, I edited your post in order for the post would be meaningful.
The function describing the height of this launched object (in meters over the sea level) versus time is
h(t) = -5t^2 + 80t.
To find the time it takes the flare to fall back and to get the sea level is
h(t) = 0, or -5t^2 + 80t = 0.
We factor it
5t(16-t) = 0
and find two roots t= 0 and t= 16.
First root is not interesting for us (it describes the starting moment).
The other root, t= 16 seconds, is the solution to the problem.
ANSWER. The flare will fall back to the sea in 16 seconds.
Solved.
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To see many other solved similar and different problems and to learn the subject deeper, wider and better, see the lessons
- Introductory lesson on a projectile thrown-shot-launched vertically up
- Problem on a projectile moving vertically up and down
- Problem on an arrow shot vertically upward
- Problem on a ball thrown vertically up from the top of a tower
- Problem on a toy rocket launched vertically up from a tall platform
Consider these lessons as your textbook, handbook, tutorials and (free of charge) home teacher.
Read them attentively and learn how to solve this type of problems once and for all.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this textbook under the topic "Projectiles launched/thrown and moving vertically up and dawn".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.