Question 1140349
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<pre>
(a)  it is  at t= 0:  s(0) = 2  feet.



(b)  find the maximum of the quadratic function.


     t = x = {{{-b/(2a)}}} = {{{-112/(2*(-16))}}} = {{{112/32}}} = 3.5 seconds



(c)  {{{s[max]}}} = s(3.5) = {{{-16*3.5^2 + 112*3.5 + 2}}} = 198 feet



(d)  s(t) = 0:   -16*t^2 + 112*t + 2 = 0


                  8t^2 - 56t - 1 = 0


                  t = {{{(56 +- sqrt(56^2 + 4*8))/(2*8)}}} = {{{(56 +- 56.285)/16}}}.


                  Only positive root works  t = {{{(56+56.285)/16}}} = 7.02 seconds.
</pre>

Solved. All question are answered.


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For details, see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Problem-on-a-projectile-moving-vertically.lesson>Problem on a projectile moving vertically up and down</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Problem-on-projectile-shooted-vertically-upward.lesson>Problem on an arrow shot vertically upward</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Typical-problems-on-an-projectile-moving-vertically-up-and-down.lesson>Problem on a ball thrown vertically up from the top of a tower</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Problem-on-a-toy-rocket-launched-vertically-up--from-the-top-of-a-platform.lesson>Problem on a toy rocket launched vertically up from a tall platform</A>


Consider these lessons as your textbook, &nbsp;handbook, &nbsp;tutorials and &nbsp;(free of charge) &nbsp;home teacher.
Read them attentively and learn how to solve this type of problems once and for all.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this textbook under the topic "<U>Projectiles launched/thrown and moving vertically up and dawn</U>".



Save the link to this online textbook together with its description


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https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


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