# An Empire State Penny of Mind

When I was ten years old, my family took a trip to New York City where I got to see one of the city’s most famous tourist traps: the Empire State Building. The view at the top of the skyscraper was incredible, spanning lengths of city for miles. I remember thinking that it’d be an awfully long drop from the top of the building to the pavement below. Since that trip, I’ve become aware of the circulated legend that a penny dropped off the top of the Empire State Building would kill a person if it hit them. It always seemed strange to me that such a tiny object could deliver a killing blow just because it’s dropped from a staggering height. However, I decided to put my intuition to the test and use science to determine whether or not my skepticism was warranted. So, will a penny dropped off the top of Empire State Building kill a person if it hits them?

Now that I had my question, I decided to form a hypothesis: If a penny is dropped off the Empire State Building, it will reach a velocity high enough to kill a person upon impact. This is the alternative hypothesis, while the null hypothesis proposes that nothing is going on, and a penny dropped at the height of the Empire State Building will not reach a velocity high enough to kill someone.

In this case, the causal variable (independent x) is the height at which the penny is dropped. The Empire State Building is 103 stories tall, making it 1,250 feet, or 381 meters in the rest of the world, to the top floor where the penny would be launched. The response variable (dependent y) is the velocity the penny reaches, as the velocity depends on the x variable of height. This makes the y variable a soft endpoint, and it is more easily measured. Ultimately, we are more concerned with the hard endpoint, which would be death if the penny reaches a velocity high enough to kill someone. However, an experiment designed to test the death of a person as the response variable would be pretty unethical, as it would be putting the test subjects at immense risk. Therefore, scientists can really only perform more theoretical tests that look at the physics behind a penny in free fall.

The response variable in this scenario is the basis for how this myth even began. In theory, a penny traveling in free fall from that kind of height would reach a deadly velocity. This is assumed to be because of the force of gravity. A kinematic equation, or an equation measuring the motion of an object, can describe this particular situation:

The equation that applies to this free fall theory is the one on the bottom left, which translates to final velocity = initial velocity + acceleration * time. To solve for this equation, the same site that gave me the formula notes that the initial velocity will be 0 meters per second, 0 m/s, because it is not moving at first. The acceleration of an object in free fall is always, in theory, -9.8 m/s. This accounts for the impact of gravity on the object. According to this article, it would take around 9 seconds for a penny dropped from the Empire State Building to hit the ground. So, according to my calculation using the formula, a penny would reach around 88 m/s, which is about 196 mph. While that is a pretty fast velocity, it’s still not enough to kill someone.

My calculation is also only accurate if we lived in a vacuum and any air resistance was removed. That is obviously not the case, and we must take the impact of drag and air resistance into account. At a certain point, an object reaches its terminal velocity, which occurs when air resistance is equivalent to the force of gravity. At terminal velocity, a penny would reach its maximum velocity, and the velocity would not go any higher. According to this paper compiled by members of the Department of Physics and Astronomy at the University of Leicester, their calculations indicate that a penny would reach its terminal velocity at 40.1 m/s, which is 89.7 mph. This is significantly lower than the original calculation that only took gravity into account, and this velocity certainly isn’t enough to kill someone.

An experiment done by Louis Bloomfield, a physics professor at the University of Virginia, comes to a similar conclusion the theoretical calculations show. In his experiment, Bloomfield used a large weather balloon full of helium to launch pennies from a dispenser at varying heights. In this study, Bloomfield is manipulating the x variable, height, to determine the terminal velocity of a falling penny, which is the y variable. What he found from this study was that despite the balloon being placed at different heights, the pennies reached their full speed around 50 feet, then never got any faster. At that height, the penny reaches its terminal velocity and simply floats to the ground from there.

A famous show on the Discovery Channel, Mythbusters, also conducted an experiment on this topic. The stars of the show, Jamie and Adam, created a gun that would launch a penny at a speed of around 64.4 m/s, which is what some other studies have suggested the terminal velocity of a penny in free fall is; it is a bit high compared to some calculations. Jamie and Adam then tested their penny gun by firing it at a skull made of gel to see if it would have an impact. Even at 64.4 m/s, or 144 mph, the penny broke through the gel layer, but didn’t even make a dent in the actual makeshift skull. This evidence is compelling when considering the possibility of death by penny, and in light of this test, it seems not likely.

Based on my research into this myth, the superstitious can rest easy. While a penny falling from a skyscraper like the Empire State Building would reach a velocity that may be enough to feel painful, it won’t be the cause of your death. Taking air resistance into account, a penny physically cannot reach a high enough velocity to deliver a fatal blow. Even though scientists can’t ethically conduct studies where they drop pennies to see if people die from it, the physics here seems sound enough to allow me to fail to reject my null hypothesis. So next time you walk through New York City, don’t be afraid of falling pennies—they won’t bite.

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