Question 1058712
.
A projectile is fired upward from the ground with an initial velocity of 76 ft/sec.  At the same instant, another projectile 
is fired upward with an initial velocity of 41 ft/sec from a roof 140 feet above the ground.

a. After how long will the two projectiles be the same height above the ground?

b. How high above the ground are the two projectiles at that time?

Please help thank you!
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<pre>
1.  An expression for the height (in feet) over the ground level for the first projectile is

    {{{H[1](t)}}} = {{{-16t^2 + 76t}}}


    An expression for the height (in feet) over the ground level for the second projectile is

    {{{H[2](t)}}} = {{{-16t^2 + 41t+140}}}.
</pre>

a)  After how long will the two projectiles be the same height above the ground?


<pre>
    It will happen when {{{H[1](t)}}} = {{{H[2](t)}}}, which gives you an equation

    {{{-16t^2 + 76t}}} = {{{-16t^2 + 41t+140}}}.

    Simplify and solve it for t:

    76t - 41t = 140  --->  35t = 140  --->  t = {{{140/35}}} = 4.
</pre>

<U>Answer</U>. It will happen in  4 seconds after the launch.



b) How high above the ground are the two projectiles at that time?


<pre>
    Simply substitute t=4 into any of the two expressions for {{{H[1]}}}, {{{H[2]}}}. For example, using {{{H[1]}}}, you will get

    {{{H[1](4)}}} = {{{-16*4^2 + 76*4}}}.

    Please complete this calculation on your own.
</pre>


There is a bunch of similar solved problems in 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>

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 textbook under the topic "<U>Projectiles launched/thrown and moving vertically up and dawn</U>".