Question 852983
The equation is:
{{{ h(t) = -16t^2 + 50t + 4 }}}
where {{{ t }}} is in seconds and {{{ h }}} is in feet
Note that when {{{ t = 0 }}}, {{{ h(t) = 4 }}} 
as it should
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You need to find {{{ t }}} when {{{ h(t) = 10 }}}
{{{ 10 = -16t^2 + 50t + 4 }}}
{{{ -16t^2 + 50t - 6 = 0 }}})
{{{ -8t^2 + 25t - 3 = 0 }}}
Use the quadratic formula
{{{ t = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = -8 }}}
{{{ b = 25 }}}
{{{ c = -3 }}}
{{{ t = (-25 +- sqrt( 25^2 - 4*(-8)*(-3) )) / (2*(-8)) }}}
{{{ t = (-25 +- sqrt( 625 - 96 )) / (-16 ) }}}
{{{ t = (-25 +- sqrt( 529 )) / (-16 ) }}}
{{{ t = (-25 +- 23) / (-16 ) }}}
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{{{ t = -48 / (-16) }}}
{{{ t = 3 }}} sec
This is the answer I want, the other answer is the time
immediately after the cannon is fired:
{{{ t = -2/(-16) }}}
{{{ t = 1/8 }}}
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The acrobat hits the net 3 sec after the cannon fires
Here's the plot:
{{{ graph( 500, 500, -1, 5, -5, 50, 10, -16x^2 + 50x + 4 ) }}}