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 dropped from a height of 300 m and that Superman can accelerate straight upward at 14.0 m/s2, determine how far Lois falls before he catches her.

Determine how long Superman takes to reach her. (in seconds)

Determine their speeds at the instant he reaches her. in m/s)

Explanation / Answer

H = 300 m
Initial Velocity = 0
Acceleration, a = 9.8 m/s^2
Let she fall's Distance h before getting rescued by Superman.

Now,
s = u*t + 1/2 * a *t^2
h = 0 + 1/2 * 9.8 * t^2
h = 4.9 t^2 ----------1

For Superman,
Initial Speed = 0
Acceleration = 14.0 m/s^2
Distance = 300 - h

s = u*t + 1/2 * a *t^2
300 - h = 0 + 1/2 * 14 t^2
Substituing Value of h from eq1
300 - 4.9 t^2 = 7 t^2
300 = 11.9 t^2
t =  5.02 s
Time Superman takes to reach her, t = 5.02 s

Final Speed of Lois Lane =
v = u + a*t
v = 0 + 9.8 * 5.02
v LoisLane =  49.2 m/s

Final Speed of Superman =
v = u + a*t
v = 0 + 14 * 5.02
v superman = 70.28 m/s

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.