Question 703113
It looks like he jumped up a little bit.
He jumped at {{{ t = 0 }}}
{{{ h(0) = -16*0^2 + 16*0 + 480 }}}
{{{ h(0) = 480 }}} ( the height of the cliff )
and
{{{ h(1) = -16*1^2 + 16*1 + 480 }}}
{{{ h(1) = -16 + 16 + 480 }}}
{{{ h(1)  = 480 }}} ( he's going back down after jumping up )
His peak is at the 1/2 point of the two times
{{{ ( 0 + 1 ) / 2 = 1/2 }}}
His peak is at {{{ t = 1/2 }}} sec
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That peak is:
{{{ h(1/2) = -16*(1/2)^2 + 16*(1/2) + 480 }}}
{{{ h(1/2) = -4  + 8 + 480 }}}
{{{ h(1/2) = 484 }}}  ft
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Jason hit the water when {{{ h = 0 }}}
{{{ 0 = -16t^2 + 16t + 480 }}}
{{{ -t^2 + t  + 30 = 0 }}}
{{{ t^2 - t - 30 = 0 }}}
{{{ t^2 - t = 30 }}}
{{{ t^2 - t + (-1/2)^2 = 30 + (-1/2)^2 }}}
{{{ t^2 - t  + 1/4 = 30 + 1/4 }}}
{{{ ( t - 1/2 )^2 = 121/4 }}}
Take the square root of both sides
{{{ t - 1/2 = 11/2 }}}
{{{ t = 1/2 + 11/2 }}}
{{{ t = 12/2 }}}
{{{ t = 6 }}}
He hit the water in 6 sec
here's the plot:
{{{ graph( 400, 400, -1, 7, -50, 550, -16x^2 + 16x + 480 ) }}}