Question 1053466
{{{ d(t) = -t^2 + 20t + 5 }}}
given:
{{{ d(t) = 100 }}}
{{{ 100 = -t^2 + 20t + 5 }}}
{{{ -t^2 + 20t - 95 = 0 }}}
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{{{ t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = -1 }}}
{{{ b = 20 }}}
{{{ c = -95 }}}
{{{ t = ( -20 +- sqrt( 20^2-4*(-1)*(-95) ))/(2*(-1)) }}}
{{{ t = ( -20 +- sqrt( 400 - 380 ))/( (-2) ) }}}
{{{ t = ( -20 +- sqrt( 20 ))/( (-2) ) }}}
{{{ t = ( -20 - 4.472 ) / (-2) }}}
{{{ t = 24.472 / 2 }}}
{{{ t = 12.236 }}}
and also:
{{{ t = ( -20 + 4.472 )/(-2) }}}
{{{ t = 15.528/2 }}}
{{{ t = 7.764 }}}
After 7.764 sec and 12.236 sec the toy plane is 100 m
from the controler
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Heres the plot:
{{{ graph( 500, 500, -4, 40, -15, 150, -x^2 + 20x + 5 ) }}}
Note that the peak is at {{{ t = 10 sec }}} and {{{ d = 105 }}} m
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The times I came up with should be below and above {{{ t = 10 }}}
by the same amount
{{{ 10 - 7.764 = 2.236 }}}
and
{{{ 12.236 - 10 = 2.236 }}}
OK