# Problem: Determined to test the law of gravity for himself, a student walks off a skyscraper 180 m high, stopwatch in hand, and starts his free fall (zero initial velocity). Five seconds later, Superman arrives at the scene and dives off the roof to save the student.Superman leaves the roof with an initial speed v0 that he produces by pushing himself downward from the edge of the roof with his legs of steel. He then falls with the same acceleration as any freely falling body. What must the value of v0 be so that Superman catches the student just before they reach the ground?If the height of the skyscraper is less than some minimum value, even Superman cant reach the student before he hits the ground. What is this minimum height?

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###### Problem Details

Determined to test the law of gravity for himself, a student walks off a skyscraper 180 m high, stopwatch in hand, and starts his free fall (zero initial velocity). Five seconds later, Superman arrives at the scene and dives off the roof to save the student.

Superman leaves the roof with an initial speed v0 that he produces by pushing himself downward from the edge of the roof with his legs of steel. He then falls with the same acceleration as any freely falling body. What must the value of v0 be so that Superman catches the student just before they reach the ground?

If the height of the skyscraper is less than some minimum value, even Superman cant reach the student before he hits the ground. What is this minimum height?