Lois Lane is pushed out of a window 300 ft above the street below. Superman is 0

Question

Lois Lane is pushed out of a window 300 ft above the street below. Superman is 0.5 miles away when he hears Lois scream and rushes to save her. He swoops down in the nick of time when Lois is just 3 feet above the ground and stops her just at ground level. Calculate the time it takes for Superman to stop Lois' fall. Assume Superman applies a constant force to Lois in breaking her fall and that she weights 120 lbs. Also, could she survive the force Superman applies to her if the human body can only withstand a maximum impulse of 20,000 N.s

Explanation / Answer

The time it takes for Lois Lane to fall from 300 ft to 3ft can be calculated using the following kinematic equation:

s = ut + 1/2at2

Here, s = 297 ft = 90.53 m, u = 0, a = 9.81 m/s

t = (2s/a) = (2*90.53/9.81) = 4.3 s

The total impulse force experienced by Lois Lane would equal the change in momentum.

= m(u - v)

m = 120 lbs = 54.43 kg, v = 0

u can be calculated as,

u = (2gh) = (2*9.81*90.53) = 42.14 m/s

The total impulse force would be mu = 54.43*42.14 = 2293.7 N.s

Since this is less than 20000 N.s she would survive.

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