From street level, superman spots Lois Lane in trouble the evil villain, Lex Lut

Question

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 dropping from a height of 300 m and that superman can accelerate straight upward at 15.0 m/s^2, 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 there 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. 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 dropping from a height of 300 m and that superman can accelerate straight upward at 15.0 m/s^2, 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 there 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

At the instant when Lois is dropped, time t=0s

At time t s, superman reaches Lois and catches her and rescues her.

So, distance travelled by superman+distance travelled by Lois is t1 time = 300m

or,using s=ut+1/2*a*t^2, 0.5*15*t^2 + 0.5*9.8*t^2 = 300

or,(b) Time superman takes to reach her = t=4.91s

In 4.91s,using s=ut+1/2*a*t^2, Lois falls s=0.5*9.8*4.91^2

or,(a) Distance Lois falls before he catches her = 118.67m

(c)Speed of superman at the instant he reaches her, by using v=u+at, is v=0+15*4.91= 73.65m/s

Speed of Loisat the instant he reaches her, by using v=u+at, is v=0*9.81*4.91=48.16m/s

These speeds are very high for falling object and for a human, this might be dangerous, and at the moment they reach each other, their direct collision should be avoided, and one way would be for superman to manoeuvre his flight and slow down at last. All this things followed, Lois can be saved.

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