Question 1035819
The rock hits the water when {{{ h = 0 }}}
{{{ h = -16t^2 + 52t + 48 }}}
{{{ 0 = -16t^2 + 52t + 48 }}}
Divide both sides by {{{ 4 }}}
{{{ -4t^2 + 13t + 12 = 0 }}}
Use quadratic formula
{{{ t = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}} 
{{{ a = -4 }}}
{{{ b = 13 }}}
{{{ c = 12 }}}
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{{{ t = ( -13 +- sqrt( 13^2 - 4*(-4)*12 )) / (2*(-4)) }}} 
{{{ t = ( -13 +- sqrt( 169 + 192 )) / (-8) }}} 
{{{ t = ( -13 +- sqrt( 361 )) / (-8) }}} 
{{{ t = ( -13 - 19 ) / (-8) }}}
{{{ t = ( -32 ) / (-8 ) }}}
{{{ t = 4 }}}
Note that I had to use the negative square root of {{{ 361 }}}
so that {{{ t }}} came out to be positive
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The rock takes 4 sec to hit the water
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Here's the plot:
{{{ graph( 400, 400, -2, 6, -10, 100, -16x^2 + 52x + 48 ) }}}