Question 776285
{{{ h = 56t - 5t^2 }}}
The first term, {{{ 56t }}} has nothing to do with gravity,
just the upward velocity of the stone
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The 2nd term has only to do with the downward
force of gravity
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The stone will be at a height of {{{ 50 }}} m on its
way up and also again on its way down
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Solve for {{{ h = 50 }}}
{{{ 50 = 56t - 5t^2 }}}
{{{ -5t^2 + 56t = 50 }}}
Divide both sides by {{{ -5 }}}
{{{ t^2 + (-56/5)*t = -10 }}}
Complete the square:
{{{ t^2 - (56/5)*t + ( 28/5 )^2 = -10 + ( 28/5 )^2 }}}
{{{ t^2 - (56/5)*t + ( 28/5 )^2 = -250/25 + 784/25 }}}
{{{ t^2 - (56/5)*t + ( 28/5 )^2 = 534/25 }}}
{{{ ( t - 28/5 )^2 = 534/25 }}}
Take the square root of both sides
{{{ t - 28/5 = -23.108/5 }}}
{{{ t = ( 28 - 23.108 ) / 5 }}}
{{{ t = .978 }}}
And also, taking the positive square root 
of the right side:
{{{ t - 28/5 = 23.108/5 }}}
{{{ t = 51.108/5 }}}
{{{ t = 10.222 }}}
The rock is at a height of 50 m at .978 sec
and also at 10.222 sec
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Here's the plot:
{{{ graph( 400, 400, -2, 12, -20, 170, -5x^2 + 56x ) }}}
The points ( .978, 50 ) and ( 10.222, 50 )
look very possible. Hope this helps.