From street level, Superman spots Lois Lane in trouble— the evil villain, Lex Luthor, is dropping her from near the top of the Empire State Building. At that very instant, the Man of Steel starts upward at a constant acceleration to attempt a midair rescue of Lois. Assuming she was dropped from a height of 300 m and that Superman can accelerate straight upward at 15.0 m/s2, determine
(a) How far Lois falls before he catches her,
(b) How long Superman takes to reach her, and
(c) Their speeds at the instant he reaches her. Comment on whether these speeds might be a danger to Lois, who, being a mere mortal, might get hurt running into the impervious Man of Steel if the speeds are too great.