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# Math

I was in two units in the United States Air Force where regulations, just about all of them, were waived. The mission was so important, we were told, that if we needed to deviate from a rule or regulation that we should use our best judgement and press on. The problem is that not all pilots possess the same high level of judgement and sometimes that is just in the eye of the beholder.

Quite often the other pilot would say "that's waived," when it just couldn't be. I often replied, "you can't waive the laws of physics." But not everyone understands this. Why? I blame the movie Superman. We saw this in a theater when it was the number one box office hit. At one point Lois Lane is falling from atop the Daily Planet office building to her certain death. Superman changes into his tights and soars up to catch her. (Video: Superman Catches Lois) At that point I said, too loudly I guess, "Now she's twice as dead."

My fellow movies goers didn't appreciate that.

Given: Empire State Building height = 1250'

Assumption: The Daily Planet Building = 1/2 Empire State Building = 625'

Formula for distance fallen d due to gravity for a given time t:

$d=½g{t}^{2}$

Time for Lois Lane to fall from top to bottom of the building:

$t=\sqrt{\frac{2d}{g}}=\sqrt{\frac{2\left(625\right)\mathrm{ft}}{32\mathrm{ft/sec²}}}=6.25\mathrm{seconds}$

Time for Lois Lane to fall from top of the building to Superman's arms (halfway down):

$t=\sqrt{\frac{2d}{g}}=\sqrt{\frac{2\left(½\right)\left(625\right)\mathrm{ft}}{32\mathrm{ft/sec²}}}=4.42\mathrm{seconds}$

Velocity v at time t while falling:

$v=gt$

Lois Lane's velocity at ground impact:

Lois Lane's velocity when caught by Superman:

Formula for distance covered d when accelerating at a for a given time t:

$d=½a{t}^{2}$

Given: Superman's time to reach Lois from ground = 10 seconds

(Timed from video = 20 seconds, figure this is doubled for dramatic effect, so actual time should be half.)

Superman's acceleration to half-way up the building:

Superman's velocity at half the distance to the top of the building:

Given: Distance from Lois Lane's head to her feet: 5 feet

Time for Lois Lane's head to hit pavement once feet hit:

Time for Lois Lane's head to reach her feet if caught by Superman:

Lois Lane's G-Load on impact with concrete:

Lois Lane's G-Load on impact with Superman:

### Math

For more about the mechanics and physic used here, see Mechanics.

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