Question 1054872
The bullet will hit the ground, which is
{{{ 100 }}} ft below the cliff ) when {{{ h(t) = 0 }}}
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{{{ h(t) = -16t^2 + 396t + 100 }}}
{{{ 0 = -16t^2 + 396t + 100 }}}
{{{ -4t^2 + 99t + 25 = 0 }}}
Use quadratic formula
{{{ t = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = -4 }}}
{{{ b = 99 }}}
{{{ c = 25 }}}
{{{ t = (-99 +- sqrt( 99^2 - 4*(-4)*25 )) / (2*(-4)) }}}
{{{ t = (-99 +- sqrt( 9801 + 400 )) / (-8) }}}
{{{ t = (-99 +- sqrt( 10201 )) / (-8) }}}
{{{ t = (-99 - 101) / (-8) }}}
{{{ t = ( -200 ) / (-8) }}}
{{{ t = 25 }}}
The bullet hits the ground in 25 sec
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check:
{{{ -4t^2 + 99t + 25 = 0 }}}
{{{ -4*25^2 + 99*25 + 25 = 0 }}}
{{{ -2500 + 2475 + 25 = 0 }}}
{{{ -2500 + 2500 = 0 }}}
{{{ 0 = 0 }}}
OK
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Here's the plot. Note that it starts at {{{ h(0) = 100 }}}
as it should
{{{ graph( 500, 500, -5, 30, -300, 3000, -16x^2 + 396x + 100 ) }}}