Question 1093126
Since the rock is tossed from a height above
20 ft, then the rock will be falling at 20 ft
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{{{ h(t) = -16t^2 + 10t + 30 }}}
{{{ 20 = -16t^2 + 10t + 30 }}} 
{{{ -16t^2 + 10t + 10 = 0 }}}
{{{ -8t^2 + 5t + 5 = 0 }}}
Use quadratic formula
{{{ t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = -8 }}}
{{{ b = 5 }}}
{{{ c = 5 }}}
{{{ t = (-5 +- sqrt( 5^2-4*(-8)*5 ))/(2*(-8)) }}}
{{{ t = (-5 - sqrt( 25 -( -160 ) ) ) / (-16) }}}
{{{ t = ( -5 - sqrt( 185 ) ) / (-16) }}}
{{{ t = ( -5 - 13.601 ) / (-16) }}}
{{{ t = 18.601/16 }}}
{{{ t = 1.163 }}} sec
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check answer:
here's the plot:
{{{ graph( 400,400, -1,3, -5,40, -16x^2 + 10x + 30 ) }}}
Looks about right