Compute all parts of given question:
Question: A juggler performs in a room whose ceiling is a height 4.0m above the level of his hands. He throws a ball upward so that it just reaches the ceiling.
Question I: What is the initial velocity?
Question II: What is the time required for the ball to reach the ceiling?
Question III: At the instant when the first ball is at the ceiling, he throws a second ball upward with two-thirds the initial velocity of the first. How long after the second ball is thrown did the two balls pass each other?
Question IV: At what distance above the juggler's hand do they pass each other?
Please provide a detailed equation on how you got the answer. Thanks.