Question 994201
You want to know the values of {{{ t }}} when
{{{ s(t) > 170 }}}
{{{ s(t) = -16t^2 + 32t + 170 }}}
When {{{ t = 0 }}},
{{{ s(0) = -16*0 + 32*0 + 170 }}}
{{{ s(0) = 170 }}}
So, {{{ t = 0 }}} is the initial time
Now you have to find {{{ t }}} when theball is
coming down and is back to the 170 ft level
{{{ s(t) = 170 }}}
{{{ 170 = -16t^2 + 32t + 170 }}}
{{{ -16t^2 + 32t = 0 }}}
{{{ t*( -16t + 32 ) = 0 }}}
{{{ 16t = 32 }}}
{{{ t = 2 }}}
The ball exceeds the height of the rooftop
between 0 and 2 sec
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Here's a plot of the ball's height and time in sec
{{{ graph( 400, 400, -1, 5, -50, 250, -16x^2 + 32x + 170 ) }}}