Question 967989
There is only 1 time when the object is on the ground,
and that is when {{{ h = 0 }}}
{{{ h =  -16t^2 + 80t + 96 }}}
{{{ 0 =  -16t^2 + 80t + 96 }}}
Divide through by {{{ 16 }}}
{{{  -t^2 + 5t + 6 }}} 
{{{ ( -t + 6 )*( t + 1 ) = 0 }}}
{{{ t = 6 }}} ( time must be positive so, {{{ t }}} can't be {{{ -1 }}} )
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the object will hit the ground in 6 sec
Here's the plot:
{{{ graph( 400, 400, -2, 7, -50, 200, -16x^2 + 80x + 96 ) }}}