Terminal Velocity of a Penny

A penny is a flat object and does not weigh a lot (~2.5 g). Because of its low density, a penny does not experience much drag force. When thrown out of a building, it reaches its terminal velocity within 50 feet of drop. Let us now calculate its terminal velocity using the given equation.

\[v_{T} = \sqrt{\frac{2mg}{C\rho_{air} A}} \]

For a penny, we have the following information:

m = 2.5 g = 0.0025 kg

ρ_air = 1.29 kg/m³

C = 1.12

Diameter = 2 cm or A = 0.000314 m²

g = 9.81 m/s²

Plugging in all the values, we get.

\[ v_T = \sqrt{\frac{2 \cdot 0.0025 \hspace{1mm} kg \cdot 9.81\hspace{1mm} m/s^2}{1 \cdot 1.12\hspace{1mm} kg/m^3 \cdot 0.000314 \hspace{1mm} m^2}}\\ \Rightarrow v_T = 10.4 \hspace{1mm} m/s \hspace{1mm} \text{or} \hspace{1mm} 23.2 \hspace{1mm} mph \]

While this appears high, a penny is so light that it cannot do much harm at this speed. For a penny to create a lethal effect, it needs to plummet in an airless environment. In this case, the penny would hit the ground at 210 mph, which is high enough to break the skin.

References
- 1. Could a Penny Dropped Off a Skyscraper Actually Kill You? – Livescience.com
  2. How High Does a Building have to be for a Penny Dropped from the Top to Kill a Person on the Ground? – Wtamu.edu
  3. Can a Penny Dropped Off a Building Kill You? – Science.howstuffworks.com
  4. What Would Happen if You Were Hit by a Penny Falling from a Skyscraper? – Usatoday.com