Question 1171580
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<pre>

In this problem, we take the gravity acceleration equal to  10 m/s^ (by rounding the true value of 9.81 m/s^2).


Then the equation for the height is  

    h(t) = -5t^2 + 35t.


To answer first question, solve the equation

    -5t^2 + 35t = 25.


It is equivalent to

    5t^2 - 35t + 25 = 0,  or

     t^2 -  7t + 5  = 0

     {{{t[1,2]}}} = {{{(7 +- sqrt(7^2 - 4*5))/2}}} = {{{(7 +- sqrt(29))/2}}} = {{{(7 +- 5.385)/2}}}


There are two time moments  

    {{{t[1]}}} = {{{(7 - 5.385)/2}}} = 0.8 seconds (rounded) moving up  and  

    {{{t[2]}}} = {{{(7 + 5.385)/2}}} = 6.2 seconds (rounded) moving down.




To answer the second question, you need solve this equation

    -5t^2 + 35t = 0.


Factor left side

    -5t*(t-7) = 0


and get the root  t = 7.  So, an object will hit ground in 7 seconds.




To answer the third question, notice that the parabola has the maximum at the midpoint between its y-intersections,

that are 0 and 7.


So, the maximum height is achieved at t= {{{(0+7)/2}}} = 3.5 seconds,

and the maximum height is


    h(7.5) = -5*3.5^2 + 35*3.5 = 61.25 meters.
</pre>

Solved.  &nbsp;&nbsp;// &nbsp;&nbsp;All questions are answered.


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In this site, &nbsp;there is a bunch of lessons on a projectile thrown/shot/launched vertically up

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

&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


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.



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