Question 1184127
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For a water balloon launched from a 49-meter overlook with an initial vertical velocity of 24.5 meters per second, 
the height h in meters as a function of time t in seconds is h=−4.9t^2+24.5t+49. When will the balloon land and burst?
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<pre>
To answer the question, you should solve this equation

    h(t) = 0,  which is  -4.9t^2 + 24.5t + 49 = 0.



Divide the left side by -4.9.  You will get much more pleasant EQUIVALENT equation

    t^2 - 5t - 100 = 0.



Use the quadratic formula to find its roots

    {{{t[1,2]}}} = {{{(5 +- sqrt(25 + 4*100))/2}}} = {{{(5 +- sqrt(425))/2}}}.



Choose the positive root (and deny negative one)

    t = {{{(5 + sqrt(425))/2}}} = 12.81.



<U>ANSWER</U>.  The event will happen in 12.81 seconds.
</pre>

Solved and thoroughly explained.


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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.