Question 1063233
.
I have another tough word problem that I hope someone can show me the solutions .

A kicker punts a football from 3 feet above the ground with an initial velocity of 47 feet per second.


<pre>
1)  Write an equation that gives the height (in feet) of the football as a function of the time (in seconds) since it was punted. 

    h(t) = {{{-16t^2 + 47t + 3}}}.

    h is the height above the ground.

    I assume (! You didn't say it) that the velocity is VERTICAL velocity (directed upward)


2)  Find the height (in feet) of the football 2 seconds after the punt. 

    Substitute t= 2 into this equation.


3)  Calculate how many seconds after the punt the ball would hit the ground.

    For it, solve the equation h(t) = 0 for t, which is the same as  {{{-16t^2 + 47t + 3}}} = 0.
</pre>


There is a bunch of lessons with similar solved problems in this site:

&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>



Notice that the equations might be written differently for different unit systems.



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>".