Question 683924
It reaches the ground when {{{ h = 0 }}}
{{{ h = -16t^2 + 40t + 8 }}}
{{{ 0 = -16t^2 + 40t + 8 }}}
{{{ 0 = -2t^2 + 5t + 1 }}}
Use the quadratic formula:
{{{ t = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = -2 }}}
{{{ b = 5 }}}
{{{ c = 1 }}}
{{{ t = (-5 +- sqrt( 5^2 - 4*(-2)*1 )) / (2*(-2)) }}}
{{{ t = (-5 +- sqrt( 25 + 8 )) / (-4) }}}
{{{ t = (-5 +- sqrt( 33 )) / (-4) }}}
{{{ t = 5/4 + sqrt(33)/4 }}}
{{{ t = 1.25 + 5.7446/4 }}}
{{{ t = 1.25 + 1.4362 }}}
{{{ t = 2.686 }}} sec
Here's a plot of the function:
{{{ graph( 400, 400, -2, 4, -1, 5,  -2x^2 + 5x + 1 ) }}}