Question 1160607
You have this quadratic equation:
 
{{{h = -16t^2 + 96t}}}

{{{16t^2 -96t + h = 0}}}
 
The solution to this is always
 
{{{t = (96 +- sqrt(96^2 - 64h))/64}}}

 
and if {{{h =144ft}}}, then 

{{{t = (96 +- sqrt(96^2 - 64*144))/64}}}

{{{t = (96 +- sqrt(9216 - 9216))/64}}}

{{{t = (96 +- sqrt(0))/64}}}

{{{t = 96/64}}}

{{{t = 1.5s}}} 
 
If you want to get back to the point of departure, that's when {{{h=0}}}.

the first problem is actually the midpoint of flight, and it will take {{{ 1.5s}}} more to  get back to the point of departure

total time is {{{t = 3s}}} 

or, do it this way:


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

{{{0= -16t(t - 6)}}}


solutions:

{{{0=-16t}}}->{{{t=0}}}

{{{0= (t - 6)}}}-> {{{t=6}}}




 and the midpoint between {{{t=0}}} and {{{t=6}}} will be {{{t = 3s}}}.