.
(a) To answer this question, you need to solve this equation
80t - 16t^2 = 0,
which is the same as
t*(80 - 16t) = 0.
It has one root t= 0 and the other root t = = 5 seconds,
which is your ANSWER.
(b) The height function is a quadratic function which has the zeroes at t= 0 and t= 5.
It has the maximum at x = midpoint between the roots 0 and 5, i.e. 2.5 seconds.
So, substitute this value t = 2.5 seconds into the given height function and get your ANSWER
= 80*2.5 - 16*2.5^2 = 100 feet.
Solved.
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In this site, there is a bunch of lessons on a projectile thrown/shot/launched vertically up
- 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.