Question 1184788
.
In a soccer match, a ball is kicked from the ground with an initial velocity of 96ft/s². 
The function for the projectile motion of the ball is H(t)=-16t²+96t. 
When will the ball reach its maximum height? What is the maximum height?
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<pre>
This quadratic function is


    h(t) = -16t^2 + 96t = -16t*(t-6).


It has zeroes (y-intercepts) t= 0 and t= 6.


The maximum of this quadratic function is reached half-way between the roots  t= 0 and t= 6,

and this half-way point is t= 3 seconds.


It means that the ball reaches its maximum height at t= 3 seconds, and the maximum height is equal to


    h(3) = -16*3^2 + 96*3 = -16*9 + 96*3 = 144.


<U>ANSWER</U>.  The ball reaches the maximum height of 144 feet at the time t= 3 seconds.
</pre>

Solved and thoroughly explained.


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For better understanding, &nbsp;see the lessons

&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.