Batman, in the spirit of scientific curiosity consistent with his work in the bat cave, determines to test the

law of gravity for himself. He walks off a Gotham City skyscraper 900 ft high, stopwatch in hand, and starts his free fall. Robin, the Boy Wonder, notices that the Joker (that evil fellow!) has unfastened the Batrope, which was to have saved Batman from crashing to death by jerking him to a stop just before hitting the pavement. Clark Kent, strolling on the roof, notices the situation, and 5 seconds after Batman leaves the roof, Superman arrives at the scene and dives off the roof to save Batman. Even Superman, however, does have a crucial kinematic limitation, in that he must choose between zero initial velocity and and variable acceleration, or variable initial velocity and the same acceleration as any freely falling body. IN ALL PARTS BELOW, SHOW METHOD CLEARLY, INCLUDING EQUATION AND UNITS. a) If Superman's acceleration is that of any freely falling body, what must his initial velocity be in order that he catch Batman just before Batman reaches the ground? b) If Superman's initial velocity is zero, what acceleration must he have to catch Batman just before Batman reaches the ground? c) If the skyscraper was not tall enough, even Superman could not save Batman, since Batman would hit the ground before Superman even arrived on the scene. What is the minimum height of the building which allows Superman to save Batman.