Question 1073859
{{{ h(t) = 36 }}}
{{{ 36 = 48t - 16t^2 }}}
{{{ 9 = 12t - 4t^2 }}}
{{{ -4t^2 + 12t - 9 = 0 }}}
{{{ t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = -4 }}}
{{{ b = 12 }}}
{{{ c = -9 }}}
{{{ t = ( -12 +- sqrt( 12^2-4*(-4)*(-9) ))/(2*(-4)) }}}
{{{ t = ( -12 +- sqrt( 144 - 144 ))/(2*(-4)) }}}
{{{ t = ( -12 ) / (-8) }}}
{{{ t = 3/2 }}}
It takes 1.5 sec to reach height of 36 ft and that
must be the maximum, since there is only 1 answer
Otherwise, you would get 2 answers: one for when
it was going up, and one for when it was going down.
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Here's the plot:
{{{ graph( 400, 400, -1, 4, -5, 50, -16x^2 + 48x ) }}}