## Challenge 731 Response

# Taking a Fall

Morris J. Marshall’s “An Unexpected Delay” appears in issue 731.

Menter, a physics professor, implies that McLeod fell to the ground from the top floor of a 30-story building in two seconds. He’s lying. Discounting wind resistance, how long would such a fall really take? From what height would a fall last only two seconds? Hint: d=½gt

^{2}.

Why is the time mentioned at all? Primarily, it shows Steve Menter’s way of thinking. For him, even a gruesome suicide or murder becomes a physics problem.

But, since Menter teaches physics, one would expect him to know by heart the formula in the Challenge 731 title and make an estimate that is not off by quite so much, unless he’s making an awkward attempt to console Krista.

How long would it take Gavin McLeod — or any object of similar shape — to fall from the 30th floor of the office building?

t = (2d/g)^{½}

t = time

Let’s assume that 1 story = about 3 meters.

d (distance) = 3 meters * 30 floors or 90 meters; maybe a trifle more.

g (acceleration due to gravity) = 9.81 meters per second per second.2d = 2*90 or 180 meters.

2d/g = 180/9.81 or a little less than 18.35

Square root of 18.35 = 4.3 seconds.

Air resistance would slow Gavin’s fall slightly. Menter’s best guess would be about five seconds, not two. If Gavin had fallen from, say, the 35th floor, air resistance would have brought him to terminal velocity at about the 5th floor.

Even though time slows as one descends into a gravity well, the time difference between 90 meters and ground level would be barely perceptible even to an atomic clock. Four or five seconds might give Gavin enough time to collect his last thoughts, but not enough to resolve the equation.

Now, what if Steve Menter knows more than he’s letting on. Maybe Gavin did have only a two-second fall. How far did he fall?

d = ½gt^{2}

d = distance

g = 9.81 meters/second^{2}

½g = 4.91 approximately

t = 2 seconds

d = 4.91*(2^{2}) or 4.91*4, thus 19.64 meters or a fall from about the sixth floor.

A two-second fall should be enough to do Gavin in, but would he explode like a bomb, as one witness says? We can figure his velocity at impact, but we might need to know his mass in order to calculate the kinetic energy.

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