Question 1090948
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First you need to learn THIS:


<pre>
    When you consider the problems like this one, the correct form of the equation for the height is 

    H(t) = -16t^2 + 96t + 16.


    Notice the sign "-" (minus) at the quadratic term.

    Your writing in the post was incorrect.
</pre>


Second, all you need to do is to solve the equation  H(t) = 0,   or, which is the same,


{{{-16t^2 + 96t + 16}}} = 0.


<pre>
For it, divide both sides by 16. You will get

-t^2 + 6t + 1 = 0,    or, which is simpler (and equivalent !)

t^2 -6t -1 = 0.


{{{t[1,2]}}} = {{{(6 +- sqrt(6^2 -4*(-1)))/2}}} = {{{(6 +- sqrt(40))/2}}} = {{{3 +- sqrt(10)}}}.


Only positive root makes sense.


<U>Answer</U>.  t = {{{3 + sqrt(10)}}} seconds.
</pre>

Solved.