Answer
(a) Straight upward.
(b) The best explanation is III.
Work Step by Step
(a) You have to launch the ball vertically upwards. Namely, since you walk with the constant speed, the ball will horizontally have no acceleration in the horizontal direction as well, so the ball will fly and fall directly to your hand.
(b) The best explanation, that exactly matches what is said in (a), is III.
