Question 645947
You need to find {{{ h(t) }}} where {{{ h }}} is
the height above ground, and {{{t}}} is the time in seconds 
for the ball to hit the ground. The equation is:
{{{ h(t) = -16t^2 + 81 }}}
In words:
( height above ground ) = ( effect of gravity pulling down ) + ( starting height above ground )
Note that at {{{ t=0 }}} when the ball hasn't started dropping yet
{{{ h(0) = -16*(0^2) + 81 }}}
{{{ h(0) = 81 }}} ft ,as it should be
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When the ball hits the ground, the height is zero, so
{{{ 0 = -16t^2 + 81 }}}
{{{ 16t^2 = 81 }}}
{{{ t^2 = ( 9/4 )^2 }}}
{{{ t = 9/4 }}} and
{{{ t = 2.25 }}} sec
It takes the ball 2.25 sec to hit the ground