Question 1206162
.
In a video game, a bird is flung on a sling shot and follows a parabolic path. 
The path of the bird can be modeled by the equation h=-16t^2+55t+50 , where h
is the height of the bird and t is the amount of time, in seconds, the bird has been in the air. 
How long will it take the bird to reach a height of 40 feet in the air 
for the first time? Round your answer to the nearest hundredth.
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<pre>
From the equation, the bird starts at height of 50 feet
and moves up under gravitation at the initial vertical speed of 55 ft/s up; 
then it falls down like a stone, under gravitation.


In short words, solve this quadratic equation

    -16t^2 + 55t + 50 = 40


using the quadratic formula, and take its greatest root.


    +-------------------------------------------------------------+
    |  We take the greatest root, because, as I described above,  |
    |    when the bird is at the height 40 ft first time,         |
    |          it is at this height last time.                    |
    +-------------------------------------------------------------+


The answer is t = {{{(55 + sqrt(55^2+4*16*10))/(2*16)}}} = 1.96 seconds (rounded).
</pre>

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In this site, &nbsp;there is a bunch of lessons on a projectile thrown/shot/launched vertically up


&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>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/A-flare-is-launched-from-a-life-raft-vertically-up.lesson>A flare is launched from a life raft vertically up</A> 


Consider these lessons as your textbook, &nbsp;handbook, &nbsp;tutorials and &nbsp;(free of charge) &nbsp;home teacher.
Read them attentively and learn on how to solve this type of problems once and for all.