Question 1055462
.
a large rock is thrown upward at a velocity of 16 feet per second from the height of 96 feet above the ground. 
how many seconds after it is release does the rock reach its highest point?
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<U>Answer</U>. t = {{{16/32}}} = 0.5 second.


<U>Solution 1</U> (Physics)


<pre>
It is a uniformly decelerated movement with the initial velocity 16 ft/s and deceleration of 32 ft/s^2 (free fall acceleration). 

Hence, vertical velocity as a function of time is  u(t) = 16 - 32*t.

The maximum height is reached when u(t) = 0,  or  16 - 32t = 0,  or  t = {{{16/32}}} = 0.5 s.
</pre>

<U>Solution 2</U> (Math, Algebra-I)


<pre>
The height as the function of time is 

h(t) = {{{-(g/2)*t^2 + vt + h[0]}}} = {{{-16*t^2 + 16t + 96}}},  (*)

where g = 32 ft/s^2 is the free fall acceleration, 16 = 16 ft/s is the initial velocity and {{{h[0]}}} is the initial height.

The quadratic function (*) has the maximum at 

t = {{{-16/(2*(-16))}}} = {{{1/2}}}.

The same answer: t = 0.5 seconds.
</pre>

See the lessons

&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> 


and the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>HOW TO complete the square to find the minimum/maximum of a quadratic function</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-How-to-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>Briefly on finding the minimum/maximum of a quadratic function</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-to-find-the-vertex-of-a-quadratic-function.lesson>HOW TO complete the square to find the vertex of a parabola</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-finding-the-vertex-of-a-parabola.lesson>Briefly on finding the vertex of a parabola</A>

in this site.



Also, 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 online textbook.


The first two lessons are under the topic "<U>Projectiles launched/thrown and moving vertically up and down</U>". 


The last four lessons are under the topic "<U>Finding minimum/maximum of quadratic functions</U>".