3. From street level, Superman spots Lois Lane in trouble as the evil villain, L

Question

3. From street level, Superman spots Lois Lane in trouble as the evil villain, Lex Luthor, drops 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. (a) Assuming she was dropped from a height of 300 m and that Superman can accelerate straight upward at 15 m s , determine how far Lois falls before he catches her. (b) Determine how long Superman takes to reach her (c) Determine 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.

Explanation / Answer

Lois Lane's distance from the top: d = d0 + (1/2)at² d = (1/2)gt² d = (1/2)(9.8)t² = 4.9t² Equation A As expected, Lois Lane's distance from the top grows with time. Superman's distance from the top: d = d0 + (1/2)at² d = 300 -(1/2)(15)t² = 300 -7.5t² Equation B As expected, Superman's distance from the top shrinks with time. Set Equation A equal to Equation B and solve for t² 4.9t² = 300 -7.5t² 12.4t² = 300 t² = 300 / 12.4 t² = 24.19 Substitute t² = 24.19 into either Equation A or Equation B for your final answer: From Equation A: d = 4.9(24.19) = 119m Verify your answer by substituting into Equation B: d = 300 -7.5(24.19) = 119m So the answer is definitely 119 meters

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