The ball's velocity at time [tex]t[/tex] would be given by
[tex]v_y=v_{0y}-gt[/tex]
At its highest point, we'll have [tex]v_y=0[/tex]. We're told this occurs at [tex]t=3.5\,\mathrm s[/tex], which means
[tex]0=v_{0y}-\left(9.8\,\dfrac{\mathrm m}{\mathrm s^2}\right)(3.5\,\mathrm s)[/tex]
[tex]\implies v_{0y}=34\,\dfrac{\mathrm m}{\mathrm s}[/tex]
