The Heroic Streak
In a certain Science Fiction TV Serie, a superhero with the ability of superspeed is wandering around the city when he sees a woman hanging in the window of a building, 250 meters away from the ground, about to fall. Then, in order to save her, he accelerates up to 200 m/s and and starts running in a vertical direction (up the building). While he does that, he is capable of maintaining his speed. After he grabs the womam, he runs down the building until he reaches the ground, now accelerating and maintaining his Mechanical Energy equal to when he was at the woman's window. Approximately how fast is he, in m/s, when he reaches the ground?
Information: The superhero weights 70 kg and the woman 50 kg. Consider Gravity Acceleration g = 10 m/s²
Notes: 1. Consider that no energy is dissipated by friction or air resistance. 2. Both the superhero and the woman suffer no harm from the acceleration (Come on! It is a TV Serie!). 3. While he runs down the building, he is carrying the woman with him. 4. The answer must be up to 3 decimals.
This question was based on the TV Serie The Flash (Season 1, Episode 5)
The answer is 212.132.
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1 solution
Using the formulas of Kinetic Energy m . v²/2 and Gravitational Energy m . g . h, you will find that his Mechanical Energy at the top is 1575000 J (if you consider he is alone) or 2700000 J (if you consider the woman too). In the ground, all of his Gravitational Energy is gone, so the whole Mechanical Energy is kinetic. Now, using the Kinetic Energy formula again: 70 . v²/2 = 1575000 or 120 . v²/2 = 2700000, you will reach the conclusion that v² = 45000. The square root of 45000 is approximately 212.132, so that would be the answer.