Question 1036506
Person hits the water when height above
water  is zero {{{ h = 0 }}}
{{{ h = -16t^2 + 4t + 6 }}}
{{{ -16t^2 + 4t + 6 = 0 }}}
{{{ -8t^2 + 2t + 3 = 0 }}}
Use quadratic formula
{{{ t = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = -8 }}}
{{{ b = 2 }}}
{{{ c = 3 }}}
{{{ t = (-2 +- sqrt( 2^2 - 4*(-8)*3 )) / (2*(-8)) }}}
{{{ t = (-2 +- sqrt( 4 + 96 )) / ( -16 ) }}}
{{{ t = ( -2 - sqrt( 100 ) ) / ( -16 ) }}}
{{{ t = ( -2 - 10 ) / ( -16 ) }}}
( note that I chose the negative square root of {{{ 100 }}}
so that time, {{{t}}}, would come out positive )
{{{ t = (-12) / (-16 ) }}}
{{{ t = 3/4 }}}
After 3/4 sec, the person hits water
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here's the plot:
{{{ graph( 400, 400, -1, 1.5, -3, 12, -16x^2 + 4x + 6 ) }}}