Roger tosses a ball straight upward at v. Ignore air drag?

Answer 1

say Vi, v initial, not v
say initial height of Roger's hand is Hi
a = - g = -9.8 meters/second^2 or -32 ft/second^2 or whatever

v = Vi - g t
h = Hi + Vi t - (1/2) g t^2
at top when v = 0
t = Vi/g at top
comes back down to Hi at 2 t