Question 1129111
At ground level, {{{ h = 0 }}}
{{{ -16t^2 + 64t + 3 = 0 }}}
Use quadratic formula
{{{ t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = -16 }}}
{{{ b = 64 }}}
{{{ c = 3 }}}
{{{ t = (-64 +- sqrt( 64^2-4*(-16)*3 ))/(2*(-16)) }}}
{{{ t = (-64 +- sqrt( 4096 + 192 ))/(-32)) }}}
{{{ t = (-64 +- sqrt( 4288 ))/(-32)) }}}
{{{ t = ( -64 - 65.4828 )/(-32) }}} ( I took the neg root to end up with positive time )
{{{ t - ( -129.4828 )/(-32) }}}
{{{ t = 4.0463 }}} sec
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check answer:
Here's the plot:
{{{ graph( 600, 400, -1, 6, -5, 70, -16x^2 + 64x + 3 ) }}}