Question 1051153
.
An object is thrown straight up from the roof's edge of a 48-foot building at an initial velocity of 32 ft/s. 
How long will it take to reach the ground?
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<pre>
The governing equation is 

h(t) = -16t^2 + 32t + 48,

where t is the time after throwing, h(t) is the object height (elevation over the ground surface in feet, 
32 is the initial velocity in ft/s, 48 is the initial elevation, 16 = {{{g/2}}} a is the half of the value 
of the free fall acceleration in ft/s^2.

We need to find the value of t for which h(t) = 0,  or

-16t^2 + 32t + 48 = 0.

Divide both sides by (-16). You will get

t^2 - 2t - 3 = 0.

Factor the left side

(t-3)*(t+1) = 0.

The positive root t = 3 is the time we are seeking for.
The other root is negative, so we ignore it.

<U>Answer</U>.  It will take 3 seconds for the onject to reach the ground.
</pre>

{{{graph( 330, 330, -1.5, 5.5, -0.5, 80.5,
          -16x^2 + 32x + 48
)}}}


Plot y = {{{-16t^2 + 32t + 48}}}


For more similar solved problems see 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>".