Question 994201
{{{s(t) = -16t^2 + v[0]t + s[0]}}}
{{{v[0] = initial _velocity}}},
{{{s[0 ]= initial_ position}}},
{{{t = time}}}

given:
{{{s[0 ]=170ft}}}
{{{v[0] =32 (ft/s)}}}
{{{s(t) >s[0 ]}}}

{{{ -16t^2 + 32t + 170>170}}}=>the ball's height exceed that of the rooftop


{{{ -16t^2 + 32t + 170>170}}}

{{{-16t^2 +32t>0}}}

{{{16(t^2 -2t)= 0}}}

{{{t^2 -2t=0}}}


{{{t(t-2)=0}}}.


solutions:

{{{t = 0 }}} 

and

{{{t = 2 }}}



so between {{{t=0}}} and {{{t=2}}} at the ball’s height exceed {{{170ft}}}