Question 1142926
{{{ d(t) = -9.8t^2 - 15t + 100 }}}
The ball is thrown downward at {{{ t=0 }}}
{{{ d(0) = -9.8*0^2 - 15*0 + 100 }}}
{{{ d(0) = 100 }}} so, the cliff is 100 m high
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What is  {{{ t }}} when {{{ d(t) = 0 }}}
{{{ -9.8t^2 - 15t + 100 = 0 }}}
{{{ t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{ a = -9.8 }}}
{{{ b = -15 }}}
{{{ c = 100 }}}
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{{{ t = (-(-15) +- sqrt( (-15)^2-4*(-9.8)*100 ))/(2*(-9.8)) }}} 
{{{ t = ( 15 +- sqrt( 225 + 3920 ))/(-19.6) }}} 
{{{ t = ( 15 +- sqrt( 4145 ))/(-19.6) }}} 
{{{ t = ( 15 + 64.3817 ) / (-19.6 ) }}} 
can't use this result since the answer is negative
{{{  t = ( 15 - 64.3817 ) / (-19.6 ) }}} 
{{{ t = -49.3817 / ( -19.6 ) }}}
{{{ t = 2.5195 }}} sec
The ball hits the ground in 2.52 sec ( rounded off )
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Note that the problem is not stated correctly.
{{{ d(t) }}} is not the distance that the ball travels,
but it is the distance above ground from {{{ t = 0 }}} sec
to {{{ t = 2.52 }}} sec
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Check:
Does {{{ d( 2.52 ) = 0 }}}?
{{{ d( 2.52 ) = -9.8*2.52^2 - 15*2.52 + 100 }}}
{{{ d( 2.52 ) = -62.234 - 37.8 + 100 }}}
{{{ d( 2.52 ) = -100.034 + 100 }}}
{{{ d( 2.52 ) = -.034 }}}
The error is due to rounding off
OK