Question 1005220
{{{ h(t)= -16t^2 + 64t +260 }}}
(a)
{{{ h(t) = 320 }}}
{{{ 320 = -16t^2 + 64t +260 }}}
{{{ -16t^2 + 64t - 60 = 0 }}}
{{{ -4t^2 + 16t - 15 = 0 }}}
use quadratic formula
{{{ t = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}} 
{{{ a = -4 }}}
{{{ b = 16 }}}
{{{ c = -15 }}}
{{{ t = ( -16 +- sqrt( 16^2 - 4*(-4)*(-15) )) / (2*(-4)) }}} 
{{{ t = ( -16 +- sqrt( 256 - 240 )) / (-8 ) }}} 
{{{ t = ( -16 +- sqrt( 16 ) ) / (-8) }}}
{{{ t = ( -16 + 4 ) / (-8) }}}
{{{ t = 3/2 }}}
and, also:
{{{ t = ( -16 - 4 ) / (-8) }}}
{{{ t = 5/2 }}}
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The height will be 320 ft at t = 3/2 sec ( on the way up )
and t = 5/2 sec ( on the way down )
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The time of flight ends when {{{ h(t) = 0 }}} again
{{{ h(t) = -16t^2 + 64t +260 }}}
{{{ 0 = -16t^2 + 64t +260 }}}
{{{ -4t^2 + 16t + 65 = 0 }}}
{{{ t = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}} 
{{{ a = -4 }}}
{{{ b = 16 }}}
{{{ c = 65 }}}
{{{ t = ( -16 +- sqrt( 16^2 - 4*(-4)*65 )) / (2*(-4)) }}} 
{{{ t = ( -16 +- sqrt( 256 + 1040 )) / (-8 ) }}} 
{{{ t = ( -16 +- sqrt( 1296 )) / (-8 ) }}} 
{{{ t = ( -16 + 36 ) / (-8 ) }}}  ( this gives negative time -can't use )
{{{ t = ( -16 - 36 ) / (-8 ) }}}
{{{ t = 52/8 }}}
{{{ t = 6.5 }}}
The flight is over in 6.5 sec
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Here's a plot of the flight:
{{{ graph( 500, 500, -1, 8, -50, 360, -16x^2 + 64x + 260 ) }}}
( I figured out that the maximum height is 324 ft )