Question 1183278
.



The basic formula for the height as the function of time is written  INCORRECTLY  in your post.


It has a  FATAL  ERROR,  which makes the solution  NONSENSICAL.


To get the basic knowledge on the subject,  read my post to the end.



//////////////



The problems on a projectile thrown-shot-launched vertically up are very popular.


But, as I often observed, the students who meet such problems for the first time,  often write 
the basic equation incorrectly,  because they do not understand the meaning of its terms.


Therefore,  I wrote this introductory lesson specially for beginners who don't know the subject AT ALL.



<pre>
If you have the formula for a height given to you as a function of time in the form


    h(t) = -at^2 + bt + c,    (1)


where "a", "b" and "c" are real numbers, a > 0, then in this formula



    (a)  the initial height is equal to the coefficient "c" value;


    (b)  the initial velocity is the coefficient  "b" in the formula;


    (c)  the coefficient "a" value is half of the gravity acceleration.

         For the Earth conditions, the gravity acceleration is g = 9.81 m/s^2,
         if you use meters for height.

         So, in this case, when you use meters as the measure of height,   a = {{{g/2}}} = {{{9.81/2}}} m/s^2  or 5 m/s^2  (approximate numerical value).


             +--------------------------------------------------------------+
             |     It can not be 3.2 m/s^2, as it is written in your post.  |
             +--------------------------------------------------------------+



    (d)  To find the height at the time moment "t", simply substitute the value of "t" into the formula (1) and calculate.


    (e)  To find the time "t" when the height has a given value h = {{{h[0]}}}, substitute  h = {{{h[0]}}} into equation (1)

         and solve equation  


             h(t) = -at^2 + bt + c = {{{h[0]}}}.    (2)



    (f)  To find the time when the height is maximal, use the formula


             {{{t[max]}}} = {{{b/(2a)}}}.      (3)



    (g)  To find the maximal height, substitute the time value  t= {{{t[max]}}}  of the formula (3)  into the formula (1).
</pre>

What's all you need to know.



To see numerous examples of solved problems, &nbsp;look into 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>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/OVERVIEW-of-lessons-on-a-projetile-thrown-shot-launched-vertically-up.lesson>OVERVIEW of lessons on a projectile thrown/shot/launched vertically up</A>

in this site.


----------------


If this introduction is helpful to you, &nbsp;I will be happy.


If it will be not enough to you to solve the problem, &nbsp;come again,

but with one indispensable condition:  &nbsp;your equation &nbsp;<U>MUST &nbsp;be written correctly</U>.



/\/\/\/\/\/\/\/



Regarding your teacher, &nbsp;you may show him &nbsp;(or her) &nbsp;this my post.  &nbsp;&nbsp;Or, &nbsp;if you hesitate do it, 

give me his &nbsp;(or her) &nbsp;contact, &nbsp;and I will ask him &nbsp;(or her), &nbsp;why he &nbsp;(or she) &nbsp;gives wrong assignments.



<pre>
    In the country where I growth and got my school and university education,

    it was UNTHINKABLE that a Math teacher gave an incorrect assignment.

    I can not recall even one single such case.

    It was not because the teachers were absolutely perfect -  they were normal people (very professional, although).

    But the educational system itself was so perfect that failed cases were impossible to happen inside of this system.
</pre>